\sqrt[3]5*\frac{1}{\sqrt[4]{5^2}}*125=5^{\frac{1}{3}}*\frac{125}{5^{\frac{2}{4}}}=5^{\frac{1}{3}}*\frac{5^3}{5^{\frac{1}{2}}}=5^{\frac{1}{3}}*5^{3-\frac{1}{2}}=
=5^{\frac{1}{3}}*5^{2\frac{1}{2}}=5^{\frac{1}{3}}*5^{\frac{5}{2}}=5^{\frac{2}{6}}*5^{\frac{15}{6}}=5^{\frac{17}{6}}