Answer
The series converges.
Work Step by Step
We have to calculate $\rho$:
$$
\rho=\lim _{n \rightarrow \infty}\left|\frac{a_{n+1}}{a_{n}}\right|=\lim _{n \rightarrow \infty}\left|\frac{1/5^{(n+1)}}{1/5^n}\right|=1/5 \lt 1
$$
Thus the series converges.
