One 5

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

$5^{\frac{1}{2}} = \sqrt{5}$

$$ 5 = 5 $$

$$ 120 = 5! $$

Two 5s

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

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

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

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

$$ 10 = 5 + 5 $$

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

$25 = 5 \times 5$

$$ 125 = 5! + 5 $$

$600 = 5 \times 5!$

$$ 3125 = 5^5 $$

$$ 12696403353658275925965100847566516959580321051449436762275840000000000000 = 55! $$

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

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

$$ 5 = 5 - 5 + 5 $$

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

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

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

$$ 15 = 5 + 5 + 5 $$

$20 = 5 \times 5 - 5$

$30 = 5 \times 5 + 5$

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

$60 = \dfrac{5!}{ \dfrac{\ln{5} }{ \ln{ \sqrt{5} } }$

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

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

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

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

$$ 20 = 5 + 5 + 5 + 5 $$

$50 = 5 \times 5 + 5 \times 5$

$130 = 5 \times 5 \times 5 + 5$

$120 = 5 \times 5 \times 5 - 5$