5. Let the 9-element set $A=\{a+b \mathrm{i} \mid a, b \in\{1,2,3\}\}$, where $\mathrm{i}$ is the imaginary unit. $\alpha=\left(z_{1}, z_{2}, \cdots, z_{9}\right)$ is a permutation of all elements in $A$, satisfying $\left|z_{1}\right| \leqslant\left|z_{2}\right| \leqslant \cdots \leqslant\left|z_{9}\right|$, then the number of such permutations $\alpha$ is $\qquad$
According to the problem, $\left|z_{1}\right|<\left|z_{2}\right|=\left|z_{3}\right|<\left|z_{4}\right|<\left|z_{5}\right|=\left|z_{6}\right|<\left|z_{7}\right|=\left|z_{8}\right|<\left|z_{9}\right|$, thus the positions of $z_{2}, z_{3} ; z_{5}, z_{6} ; z_{7}, z_{8}$ can be swapped, so the number of such arrangements $\alpha$ is $2 \times 2 \times 2=8$.