5. For what values of $a$ does the system of equations $\left\{\begin{array}{c}(x-2-3 \cos a)^{2}+(y+2-3 \sin a)^{2}=1 \\ (y+2)(x+y)=0\end{array}\right.$ have a unique solution?
Answer: $a_{1}= \pm \arcsin \frac{1}{3}+\pi k, a_{2}=-\frac{\pi}{4} \pm \arcsin \frac{1}{3}+\pi k, k \in Z$.