Aus Online Mathematik Brückenkurs 1

It is often most appropriate to get rid of the root sign and write everything in power form, and then use the power rules,

\displaystyle \sqrt{5}\cdot\sqrt[3]{5}\cdot 5 = 5^{1/2}\cdot 5^{1/3}\cdot 5^{1} = 5^{1/2+1/3+1} = 5^{11/6}\,\textrm{.}