Answer
Converges by Direct Comparison Test
Work Step by Step
Use the Direct comparison test
$\Sigma^{\infty} _{n=1} \frac{1}{5^n +1} = a_n $
$ \Sigma^{\infty} _{n=1} \frac{1}{5^n} = b_n$
$b_n$ converges by geometric series because $|r| \lt 1$
Since, $ 0 \lt a_n \leq b_n $
$a_n$ must also converge
