7. Given that $f(x)$ is an odd function with a period of 5, $f(-3)=1$, $\tan \alpha=2$, $f(20 \sin \alpha \cdot \cos \alpha)=$ $\qquad$ .
7. -1 .
$$
\begin{array}{c}
\tan \alpha=2, \sin \alpha=2 \cos \alpha, \text { and } \cos \alpha= \pm \frac{\sqrt{5}}{5}, 20 \sin \alpha \cos \alpha=40 \cos ^{2} \alpha=8 . \\
f(20 \sin \alpha \cos \alpha)=f(8)=f(3+5)=f(3)=-f(-3)=-1 .
\end{array}
$$