5. Given that line $A B$ intersects the parabola $y^{2}=4 x$ at points $A$ and $B$, $M$ is the midpoint of $A B$, and $C$ is a moving point on the parabola. If point $C_{0}$ satisfies
$$
\overrightarrow{C_{0} A} \cdot \overrightarrow{C_{0} B}=\min \{\overrightarrow{C A} \cdot \overrightarrow{C B}\} \text {, }
$$

then the following must be true is ( ).
(A) $C_{0} M \perp A B$
(B) $C_{0} M \perp l\left(l\right.$ is the tangent line to the parabola at point $C_{0}$)
(C) $C_{0} A \perp C_{0} B$
(D) $C_{0} M=\frac{1}{2} A B$
5. B.

Notice,
$$
\begin{array}{l}
\overrightarrow{C A} \cdot \overrightarrow{C B}=(\overrightarrow{C M}-\overrightarrow{A M}) \cdot(\overrightarrow{C M}-\overrightarrow{B M}) \\
=|\overrightarrow{C M}|^{2}-\overrightarrow{C M} \cdot(\overrightarrow{A M}+\overrightarrow{B M})+\overrightarrow{A M} \cdot \overrightarrow{B M} \\
=|\overrightarrow{C M}|^{2}-|\overrightarrow{A M}|^{2} \\
\Leftrightarrow C M \perp l .
\end{array}
$$