5. For what values of $a$ does the system of equations $\left\{\begin{array}{c}(x+2+2 \sqrt{2} \cos a)^{2}+(y-1-2 \sqrt{2} \sin a)^{2}=2 \\ (x-y+3)(x+y+1)=0\end{array}\right.$ have three

solutions?
Answer: $a_{1}=\frac{7 \pi}{12}+\pi k, a_{2}=\frac{11 \pi}{12}+\pi k, k \in Z$.