5. Let the function $f(x)=x^{2}+6 x+8$. If $f(b x+c)=4 x^{2}+16 x+15$, then $c-2 b=(\quad)$.
(A) 3
(B) 7
(C) -3
(D) -7
5. C.

Take $x=-2$, we have $f(c-2b)=16-16 \times 2+15=-1$. And when $x^{2}+6x+8=-1$, we have $x=-3$. Therefore,
$$
c-2b=-3 \text{. }
$$