5. In a regular $n$-sided pyramid, the range of the dihedral angle between two adjacent lateral faces is
(A) $\left(\frac{n-2}{n} \pi, \pi\right)$
(B) $\left(\frac{n-1}{n} \pi, \pi\right)$
( C) $\left(0, \frac{\pi}{2}\right)$
(D) $\left(\frac{n-2}{n} \pi, \frac{n-1}{n} \pi\right)$
5.【Analysis and Solution】As shown in the figure, let the regular $n$-sided pyramid be $S-A_{1} A_{2} \cdots A_{n}$. Without loss of generality, assume the base regular $n$-sided polygon is fixed, and the vertex $S$ moves. The dihedral angle between two adjacent lateral faces is $\angle A_{2} H A_{n}$. When $S$ moves upward and approaches the extreme position (i.e., to the center of the base regular $n$-sided polygon), $\angle A_{2} H A_{n}$ tends to a straight angle; when $S$ moves upward and approaches infinity, the regular $n$-sided pyramid approaches a regular $n$-sided prism, and $\angle A_{2} H A_{n}$ tends to $\angle A_{2} A_{1} A_{n}=\frac{(n-2) \pi}{n}$. Therefore, $\frac{n-2}{n} \pi < \angle A_{2} H A_{n} < \pi$.