jmc

We have $$\frac{\sqrt[3]{5}}{\sqrt[5]{5}}=\frac{5^{\frac{1}{3}}}{5^{\frac{1}{5}}}=5^{\frac{1}{3}-\frac{1}{5}}=5^{\frac{2}{15}}.$$So, the expression equals 5 raised to the $\boxed{2/15}$ power.