5. The number of integer solutions to the inequality $x-1<(x-1)^{2}<3 x+7$
(A) is 4;
(B) is less than 4;
(C) is more than 5;
(D) is 5.
5. (A)
$$
\begin{array}{l}
(x-2)(x-1)>0 \Leftrightarrow x2 . \\
(x+1)(x-6)<0 \Leftrightarrow-1<x<6 .
\end{array}
$$

Therefore, the integer solutions of the original inequality are the integers between -1 and 6, excluding 1 and 2. That is, the integers $0,3,4,5$.