Answer
Eventually strictly decreasing.
Work Step by Step
Consider $$f(x)=\left\{x^5 e^{-x}\right\}$$ Then
\begin{align*}
f'(x) &=x^4 (5-x) e^{-x} \lt 0
\end{align*}
We see that $f'(x) \lt 0$ for $x \gt 5$. This implies that the given sequence is eventually strictly decreasing.