5. For which $a$ does the system

$$
\left\{\begin{array}{c}
(x-8) \sin a-(y+2) \cos a=0 \\
\left((x-3)^{2}+(y-3)^{2}-1\right)\left((x-3)^{2}+(y-3)^{2}-9\right)=0
\end{array}\right.
$$

have four solutions
Answer:

$$
a \in\left(\frac{3 \pi}{4}-\arcsin \frac{\sqrt{2}}{10}+\pi n ; \frac{3 \pi}{4}+\arcsin \frac{\sqrt{2}}{10}+\pi n\right), n \in Z
$$