5. The vertices of $\triangle A B C$ correspond to the complex numbers $z_{1}, z_{2}, z_{3}$, and $\left|z_{1}\right|=\left|z_{2}\right|=\left|z_{3}\right|=1$, express the center of the nine-point circle of $\triangle A B C$ in terms of $z_{1}, z_{2}, z_{3}$ as $\qquad$.
5. $\frac{1}{2}\left(z_{1}+z_{2}+z_{3}\right), O$ is the origin, $z_{H}=\left(z_{1}+z_{2}+z_{3}\right)$ the nine-point circle center is the midpoint of $O H$.