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

$b)\sqrt[3]{5}=5^{\frac{1}{3}}$

$c)\sqrt{125}=\sqrt{5^3}={\left(5^3\right)}^{\frac{1}{2}}=5^{\frac{3}{2}}$

$d)\sqrt[3]{25}=\sqrt[3]{5^2}={\left(5^2\right)}^{\frac{1}{3}}=5^{\frac{2}{3}}$

$e)\sqrt[4]{125}=\sqrt[4]{5^3}={\left(5^3\right)}^{\frac{1}{4}}=5^{\frac{3}{4}}$