Answer
Convergent
Work Step by Step
Ratio Test:
$\lim\limits_{n \to \infty}\frac{a_{n+1}}{a_{n}}=\lim\limits_{n \to \infty}\frac{\frac{(n+1)^{3}}{5^{n+1}}}{\frac {n^{3}}{5^{n}}}$
$=\frac{1}{5}(\frac{n+1}{n})^{3}$
$=\frac{1}{5}\lt 1$
Thus, the series is convergent.