Answer
Diverges
Work Step by Step
We have: $a_k=\dfrac{5 \ln k}{k}$ and $b_k=\dfrac{5}{k}$
Now, we can see that
$\dfrac{5 \ln k}{k} \gt \dfrac{5}{k}$ on $(e, \infty)$
But the series $\Sigma_{k=1}^{\infty} \dfrac{5}{k}$ is a harmonic series which is a divergent series .
Therefore, the series diverges by the comparison test.
