5. For what values of $a$ does the system of equations $\left\{\begin{array}{c}(x-2-\sqrt{5} \cos a)^{2}+(y+1-\sqrt{5} \sin a)^{2}=\frac{5}{4} \text { have two solutions? } \\ (x-2)(x-y-3)=0\end{array}\right.$
Answer: $a \in\left(\frac{\pi}{12}+\pi k ; \frac{\pi}{3}+\pi k\right) \cup\left(\frac{5 \pi}{12}+\pi k ; \frac{2 \pi}{3}+\pi k\right), k \in Z$.