9. If $5 \pi$ is a period of the function $f(x)=\cos n x \cdot \sin \frac{80}{n^{2}} x$, then all possible values of the positive integer $n$ are $\qquad$
$$
f(5 \pi)=\cos 5 n \pi \sin \frac{400 \pi}{n^{2}}=f(0)=0 \Rightarrow \sin \frac{400 \pi}{n^{2}}=0 \Rightarrow \frac{400 \pi}{n^{2}}=k \pi \text {, }
$$

Thus, $\frac{400}{n^{2}}=k \in \mathbf{N}^{*} \Rightarrow n=1,2,4,5,10,20$. Upon verification, $n=2,10$.