5. Let $a$, $b$, $c$ ($a<5$) be positive real numbers, and satisfy $a^{2}-a-2 b-2 c=0$ and $a+2 b-2 c+3=0$. Then the size relationship between $a$, $b$, and $c$ is ( ).
(A) $a<b<c$
(B) $b<c<a$
(C) $b<a<c$
(D) $c<a<b$
5. C.

Given $\left\{\begin{array}{l}a^{2}-a=2 b+2 c, \\ a+3=2 c-2 b .\end{array}\right.$
then $4 c=a^{2}+3$,
$$
4 b=a^{2}-2 a-3=(a-1)^{2}-4>0 \Rightarrow a>3 \text {. }
$$

Also, $a>0 \\
\Rightarrow c>a, \\
4(b-a)=a^{2}-6 a-3=(a-3)^{2}-12b .
\end{array}
$$

Therefore, $c>a>b$.