Answer
Diverges
Work Step by Step
Let $u_n=\dfrac{5^n}{(\sqrt n)(4^n)}$ and $v_n=\dfrac{ 1}{\sqrt n}$
Now, $\lim\limits_{n \to \infty}\dfrac{u_n}{v_n} =\lim\limits_{n \to \infty}\dfrac{\dfrac{5^n}{(\sqrt n)(4^n)}}{ 1/\sqrt n}$
$\implies \lim\limits_{n \to \infty} \dfrac{(\sqrt n)( 5^n)}{(\sqrt n)(4^n)}=\infty$
Therefore, the series diverges due to the limit comparison test.
