Five Fives/Table of 5s

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Zero 5s

$1=\ln {e}$

$9+4{\sqrt {5}}=\phi \left(\phi ^{5}\right)$

One 5

Various ways of arranging a single 5 to yield different numbers. (More limited than 4, of course...)

${\sqrt {5}}$

$\phi ^{n}{\sqrt {5}}=\phi ^{n+1}+\phi ^{n-1}$

Failed to parse (Conversion error. Server ("https://en.wikipedia.org/api/rest_") reported: "Cannot get mml. Server problem."): {\displaystyle -1=\cos {\left(5\pi \right)}}

Failed to parse (Conversion error. Server ("https://en.wikipedia.org/api/rest_") reported: "Cannot get mml. Server problem."): {\displaystyle 0=\sin {\left(5\pi \right)}}

Failed to parse (Conversion error. Server ("https://en.wikipedia.org/api/rest_") reported: "Cannot get mml. Server problem."): {\displaystyle 1=x^{\sin {\left(5\pi \right)}}}

$2=\phi \times \phi \times \phi -{\sqrt {5}}$

$5$

$15=5!!$

$120=5!$

Two 5s

$0=\ln {\dfrac {5}{5}}$

$1={\dfrac {5}{5}}$

$2={\dfrac {\ln {(5)}}{\ln {({\sqrt {5}})}}}$

$3=\phi ^{5}-5\phi$

$4={\dfrac {\ln {5}}{\ln {\left({\sqrt {\sqrt {5}}}\right)}}}$

$5={\sqrt {5\times 5}}$

$8={\dfrac {\ln {5}}{\ln {\left({\sqrt {\sqrt {\sqrt {5}}}}\right)}}}$

$10=5+5$

$11=\phi ^{5}-\phi ^{-5}$

Failed to parse (Conversion error. Server ("https://en.wikipedia.org/api/rest_") reported: "Cannot get mml. Server problem."): {\displaystyle 16={\dfrac {\ln {5}}{\ln {\left({\sqrt {\sqrt {\sqrt {\sqrt {5}}}}}\right)}}}}

$24={\dfrac {5!}{5}}$

$25=5\times 5$

$32={\dfrac {\ln {5}}{\ln {\left({\sqrt {\sqrt {\sqrt {\sqrt {\sqrt {5}}}}}}\right)}}}$

$55$

$115=5!-5$

$125=5!+5$

$600=5\times 5!$

Failed to parse (Conversion error. Server ("https://en.wikipedia.org/api/rest_") reported: "Cannot get mml. Server problem."): {\displaystyle 3125=5^{5}}

$11981655542024930675232002=\phi ^{5!}-\phi ^{-5!}$

$12696403353658275925965100847566516959580321051449436762275840000000000000=55!$

Three 5s

${\dfrac {1}{2}}={\dfrac {\ln {\left({\dfrac {5}{\sqrt {5}}}\right)}}{\ln {(5)}}}$

${\dfrac {3}{5}}={\dfrac {1}{5}}\left(\phi ^{5}-5\phi \right)$

${\dfrac {25}{24}}={\dfrac {5!+5}{5!}}$

$1={\dfrac {\sqrt {5\times 5}}{5}}$

$2={\dfrac {\ln {(5)}}{\ln {\left({\dfrac {5}{\sqrt {5}}}\right)}}}$

$3=\log _{5}{(5!+5)}$

$4=5-{\dfrac {5}{5}}$

$5=5-5+5$

$5={\sqrt[{5}]{5^{5}}}$

$5={\sqrt {\dfrac {\sqrt {5^{5}}}{\sqrt {5}}}}$

$5={\dfrac {5\times 5}{5}}$

$6=5+{\dfrac {5}{5}}$

Failed to parse (Conversion error. Server ("https://en.wikipedia.org/api/rest_") reported: "Cannot get mml. Server problem."): {\displaystyle 7=5+{\dfrac {\ln {\left(5\right)}}{\ln {\left({\sqrt {5}}\right)}}}}

$8=\phi ^{5}-5\phi +5$

$9=5+{\dfrac {\ln {\left(5\right)}}{\ln {\left({\sqrt {\sqrt {5}}}\right)}}}$

$10={\sqrt {5}}\left({\sqrt {5}}+{\sqrt {5}}\right)$

$11={\dfrac {55}{5}}$

$12={\dfrac {5!}{5+5}}$

$13=5!!-{\dfrac {\ln {\left(5\right)}}{\ln {\left({\sqrt {5}}\right)}}}$

$15=5+5+5$

$16=\phi ^{5}-\phi ^{-5}+5$

$18=5!!+\phi ^{5}-5\phi$

$19={\dfrac {5!}{5}}-5$

$20=5\times 5-5$

$20={\dfrac {5\lg {5}}{\lg {\left({\sqrt {\sqrt {5}}}\right)}}}$

$25={\dfrac {5!+5}{5}}$

$25={\dfrac {\sqrt {5^{5}}}{\sqrt {5}}}$

$25={\sqrt {5}}\left(\phi ^{5}+\phi ^{-5}\right)$

Failed to parse (Conversion error. Server ("https://en.wikipedia.org/api/rest_") reported: "Cannot get mml. Server problem."): {\displaystyle 25=5+5+5!!}

$26=\left(\phi ^{5}-\phi {-5}\right)+5!!$

Failed to parse (Conversion error. Server ("https://en.wikipedia.org/api/rest_") reported: "Cannot get mml. Server problem."): {\displaystyle 29={\dfrac {5!}{5}}+5}

$30=5\times 5+5$

$32=\left({\dfrac {\ln {5}}{\ln {\sqrt {5}}}}\right)^{5}$

$50=55-5$

$50=5(5+5)$

$55=5\left(\phi ^{5}-\phi ^{-5}\right)$

$60={\dfrac {5!}{\left({\dfrac {\ln {5}}{\ln {\sqrt {5}}}}\right)}}$

$95=5!-5\times 5$

$96=5!-{\dfrac {5!}{5}}$

$110=5!-5-5$

$120=5!+5-5$

$123=\phi ^{5}-5\phi +5!$

$130=5!+5+5$

$145=5!+5\times 5$

Failed to parse (Conversion error. Server ("https://en.wikipedia.org/api/rest_") reported: "Cannot get mml. Server problem."): {\displaystyle 243=\left(\phi ^{5}-5\phi \right)^{5}}

$625={\dfrac {5^{5}}{5}}$

$1024=\left({\dfrac {\ln {5}}{\ln {\sqrt {\sqrt {5}}}}}\right)^{5}$

$3005=5^{5}-5!$

Failed to parse (Conversion error. Server ("https://en.wikipedia.org/api/rest_") reported: "Cannot get mml. Server problem."): {\displaystyle 9765625=\left(5\times 5\right)^{5}}

$503284375=55^{5}$

Failed to parse (Conversion error. Server ("https://en.wikipedia.org/api/rest_") reported: "Cannot get mml. Server problem."): {\displaystyle 298023223876953125=5^{5\times 5}}

Four 5s

$1={\dfrac {\ln {\left({\dfrac {5}{\sqrt {5}}}\right)}+\ln {5}}{\ln {5}}}$

$1={\dfrac {5^{5}}{5^{5}}}$

$1={\dfrac {5\times 5}{5\times 5}}$

Failed to parse (Conversion error. Server ("https://en.wikipedia.org/api/rest_") reported: "Cannot get mml. Server problem."): {\displaystyle 6={\dfrac {\ln {(5)}}{\ln {({\sqrt {5}})}}}+{\dfrac {\ln {(5)}}{\ln {({\sqrt {\sqrt {5}}})}}}}

Failed to parse (Conversion error. Server ("https://en.wikipedia.org/api/rest_") reported: "Cannot get mml. Server problem."): {\displaystyle 7={\sqrt {{\dfrac {5!}{5}}+(5\times 5)}}}

$8=\left({\dfrac {\ln {(5)}}{\ln {({\sqrt {5}})}}}\right)\left({\dfrac {\ln {(5)}}{\ln {({\sqrt {\sqrt {5}}})}}}\right)$

Failed to parse (Conversion error. Server ("https://en.wikipedia.org/api/rest_") reported: "Cannot get mml. Server problem."): {\displaystyle 9=5+5-{\dfrac {5}{5}}}

$11=5+5+{\dfrac {5}{5}}$

Failed to parse (Conversion error. Server ("https://en.wikipedia.org/api/rest_") reported: "Cannot get mml. Server problem."): {\displaystyle 12=\left({\dfrac {5!}{5}}\right)\times \left({\dfrac {\ln {\sqrt {5}}}{\ln {5}}}\right)}

Failed to parse (Conversion error. Server ("https://en.wikipedia.org/api/rest_") reported: "Cannot get mml. Server problem."): {\displaystyle 13={\dfrac {5!-55}{5}}}

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): {\displaystyle 15 = \left( \log_{5}{ (5! + 5)^5 } \right) }

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): {\displaystyle 20 = 5 + 5 + 5 + 5 }

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): {\displaystyle 26 = \dfrac{5^5 - 5}{5!} }

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): {\displaystyle 34 = \phi^{5 + 5} - 55 \phi }

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): {\displaystyle 35 = \dfrac{55 + 5!}{5} }

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): {\displaystyle 35 = 5 \times 5 + 5 + 5 }

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): {\displaystyle 49 = \dfrac{5!}{5} + (5 \times 5) }

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): {\displaystyle 50 = 5 \times 5 + 5 \times 5 }

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): {\displaystyle 52 = 55 - \phi^{5} + 5 \phi }

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): {\displaystyle 60 = 5 \left( \dfrac{ 5! }{ 5 + 5 } \right) }

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): {\displaystyle 70 = 5! + 5 - 55 }

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): {\displaystyle 89 = \dfrac{ \phi \left( \phi^{5 + 5} \right) - 55 }{ \phi } }

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): {\displaystyle 120 = 5 \times 5 \times 5 - 5 }

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): {\displaystyle 123 = \phi^{5+5} + \dfrac{1}{\phi^{5+5}} }

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): {\displaystyle 125 = 5 \sqrt{5} \left( \phi^{5} + \phi{-5} \right) }

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): {\displaystyle 130 = 5 \times 5 \times 5 + 5 }

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): {\displaystyle 140 = 5! + (5 \times 5) - 5 }

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): {\displaystyle 150 = 5 \left( 5 \times 5 + 5 \right) }

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): {\displaystyle 160 = 5 \left( \dfrac{ \ln{5} }{ \ln{\sqrt{5}} } \right)^5 }

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): {\displaystyle 243 = \left( \log_{5}{(5! + 5)} \right) ^5 }

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): {\displaystyle ( 5_{5} )! = (10_{5})! = 440_{5} = 120_{10} }

(5 base 5 is 10 base 5; 5 base 5 factorial is 440 base 5, or 120 base 10. No surprises here.)

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): {\displaystyle 505 = \dfrac{5^5}{5} - 5! }

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): {\displaystyle 605 = 55 \left( \phi^5 - \phi^{-5} \right) }

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): {\displaystyle 3000 = \left( 5^5 - 5 \right) - 5! }

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): {\displaystyle 3025 = 55 \times 55 }

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): {\displaystyle 3070 = 5^5 - 55 }

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): {\displaystyle 3100 = 5^5 - 5 \times 5 }

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): {\displaystyle 3125 = \dfrac{5 \times 5^5}{5} }

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): {\displaystyle 161051 = 11^5 = \left( \dfrac{55}{5} \right)^5 }