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\centerdot \sqrt[3]{5}}\centerdot 5=5^{{1}/{2}\;}\centerdot 5^{{1}/{3}\;}\centerdot 5^{1}=5^{{1}/{2}\;+{1}/{3}\;+1}=5^{{11}/{6}\;}