Answer
Divergent
Work Step by Step
$\lim\limits_{n \to \infty}\sqrt[n] a_{n}=\lim\limits_{n \to \infty}\sqrt[n] {(\frac{n!}{n^{4}})^{n}}$
$=\lim\limits_{n \to \infty}\frac{n!}{n^{4}}$
$=\infty \gt 1$
The series is divergent by the root test.