Answer
Converges absolutely
Work Step by Step
Let us suppose a series $a_k$ such that $L=\lim\limits_{k \to \infty} |\dfrac{a_{k+1}}{a_k}|$ converges when $L\lt 1$ and diverges when $L \gt 1$.
Now, we have: $ L=\lim\limits_{k \to \infty} |\dfrac{a_{k+1}}{a_k}|=\lim\limits_{k \to \infty} \dfrac{k+1}{5^{k+1}} \times \dfrac{5^k}{k}\\=\lim\limits_{k \to \infty} |\dfrac{1}{5}(1+\dfrac{1}{k})| \\=\dfrac{1}{5} \lt 1$
So, we can conclude that the given series converges absolutely.
