5 Let the left and right foci of the hyperbola be $F_{1}, F_{2}$, and the left and right vertices be $M, N$. If the vertex $P$ of $\triangle P F_{1} F_{2}$ is on the hyperbola, then the point where the incircle of $\triangle P F_{1} F_{2}$ touches the side $F_{1} F_{2}$ is
A. inside the segment $M N$
B. at point $M$ or point $N$
C. inside the segment $F_{1} M$ or inside the segment $N F_{2}$
D. cannot be determined
5 B. Let the incircle of $\triangle P F_{1} F_{2}$ touch $F_{1} F_{2}$ at point $G$, touch $P F_{1}$ at $H$, and touch $P F_{2}$ at $K$. According to the problem, we have
$$
\begin{aligned}
\left|G F_{1}\right|-\left|G F_{2}\right| & =\left|H F_{1}\right|-\left|K F_{2}\right| \\
& =\left(\left|H F_{1}\right|+|H P|\right)-\left(\left|K F_{2}\right|+|K P|\right) \\
& =\left|P F_{1}\right|-\left|P F_{2}\right| .
\end{aligned}
$$

By the definition of a hyperbola, $G$ lies on the hyperbola. Since $G$ is on the line $F_{1} F_{2}$, $G$ either coincides with $M$ or with $N$.