Answer
$5\sqrt[3] (xy^{2}z^{5})$
Work Step by Step
We are told on page 419 that $a^{\frac{m}{n}}=\sqrt[n] (a^{m})$ (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, $5(xy^{2}z^{5})^{\frac{1}{3}}=5(\sqrt[3] (xy^{2}z^{5}))=5\sqrt[3] (xy^{2}z^{5})$
