Answer
$5^{\frac{1}{5}}x^{\frac{2}{5}}y^{\frac{3}{5}}$
Work Step by Step
We are told on page 419 that $\sqrt[n] (a^{m})=a^{\frac{m}{n}}$ (where m and n are positive integers greater than 1 with $\frac{m}{n}$ in simplest form and $\sqrt[n] a$ is a real number).
Therefore, $\sqrt[5] (5x^{2}y^{3})=(5x^{2}y^{3})^{\frac{1}{5}}=5^{\frac{1}{5}}x^{\frac{2}{5}}y^{\frac{3}{5}}$
