5. For which integers $a$ and $b$ does the system of equations

$$
\left\{\begin{array}{c}
|a x-2 y+b|=3 \\
(3 x-4 y-1)(4 x-y-10)(x+5 y+6)=0
\end{array}\right.
$$

have an infinite number of solutions?
Answer: $a=8, b=-17 ; a=8 ; b=-23$.