5. Let $z$ be a complex number. If $\frac{z-6}{z-8 \mathrm{i}}$ is a pure imaginary number, then the maximum value of $|\operatorname{Im} z|$ is $\qquad$ .
5.9.

Given that $\frac{z-6}{z-8 \mathrm{i}}$ is a pure imaginary number and considering the geometric meaning of complex division, we know that the point $Z$ corresponding to $z$ in the complex plane lies on the circle with $6$ and $8 \mathrm{i}$ as endpoints of its diameter (excluding the points corresponding to $6$ and $8 \mathrm{i}$). Therefore, $|\operatorname{Im} z|$ is the distance from $Z$ to the $x$-axis, and its maximum value is 9.