5. There are six thin rods, with lengths sequentially being $3$, $2 \sqrt{2}$, $2$, $2$, $2$, $2$. Use them to form a triangular pyramid. Then, the cosine value of the angle formed by the two longer edges is $\qquad$.
Thus, the two longer edges must lie in the same plane.
According to the cosine rule, we get
$$
\cos \alpha=\frac{9+8-4}{12 \sqrt{2}}=\frac{13 \sqrt{2}}{24} \text {. }
$$