若 $\sin \alpha+\cos \alpha=\frac{5}{3}, \angle \alpha$ 为锐角, 则 $\sin \alpha \cdot \cos \alpha$ 的值是
$\because \sin \mathrm{A}+\cos \mathrm{A}=\frac{5}{3}$,
$\therefore \sin ^{2} \mathrm{~A}+\cos ^{2} \mathrm{~A}+2 \sin \mathrm{A} \cos \mathrm{A}=\frac{25}{9}$, 即 $1+2 \sin \mathrm{A} \cos \mathrm{A}=\frac{25}{9}$ ，

$\therefore \sin A \cos A=\frac{8}{9}$. 故答案为 $\frac{8}{9}$