5. Given that $a$ and $b$ are integers, the linear equation in one variable $x$
$$
2 x-[2-(2 b-1) x]=a-2
$$

and $(2 b-1) x+3=7-[(2-b) x+3]$
have the same solution. Then $a b=(\quad)$.
(A) 0
(B) -6
(C) 0 or -6
(D) No solution
5. C.

From the first equation, we get $x=\frac{a}{2 b+1}$.
From the second equation, we get $x=\frac{1}{b+1}$.
Since the two equations have the same solution, we have,
$$
\begin{array}{l}
\frac{a}{2 b+1}=\frac{1}{b+1} \\
\Rightarrow a=\frac{2 b+1}{b+1}=2-\frac{1}{b+1} .
\end{array}
$$

Given that $a$ and $b$ are integers, we get $b=0$ or -2, and accordingly, $a=1$ or 3.

Therefore, $a b=0$ or -6.