5. For an equilateral triangle $ABC$ with side length $2 \sqrt{3}$, two moving points $P, M$ in its plane satisfy $|\overrightarrow{A P}|=1, \overrightarrow{P M}=\overrightarrow{M B}$, then the minimum value of $|\overrightarrow{C M}|$ is $\qquad$.
Given $A(0,0), B(2 \sqrt{3}, 0), C(\sqrt{3}, 3)$, then $P(\cos \theta, \sin \theta), M\left(\sqrt{3}+\frac{1}{2} \cos \theta, \frac{1}{2} \sin \theta\right)$. That is, point $M$ lies on the circle with center $(\sqrt{3}, 0)$ and radius $\frac{1}{2}$, so $|\overrightarrow{C M}|_{\text {min }}=3-\frac{1}{2}=\frac{5}{2}$.