$\sin 5 \theta \cos 3 \theta=\sin 9 \theta \cos 7 \theta$

$\Rightarrow 2 \sin 5 \theta \cos 3 \theta=2 \sin 9 \theta \cos 7 \theta$

$\Rightarrow \sin 8 \theta+\sin 2 \theta=\sin (16 \theta)+\sin 2 \theta$

$\Rightarrow \sin 8 \theta-\sin 16 \theta=0$

$\Rightarrow \sin 8 \theta(1-2 \cos 8 \theta)=0$

$\Rightarrow \sin 8 \theta=0$ or $\cos 8 \theta=\frac{1}{2}$

$\Rightarrow 8 \theta=n \pi$ or $8 \theta=2 n \pi \pm \frac{\pi}{3}$

$\Rightarrow \theta=\frac{n \pi}{8}$ or $\theta=\frac{2 n \pi}{8} \pm \frac{\pi}{24}$

Therefore number of values of $\theta$ is 5