5. Let $P$ be any point on the ellipse $\frac{x^{2}}{16}+\frac{y^{2}}{9}=1$ other than the endpoints of the major axis, $F_{1}, F_{2}$ be its left and right foci, and $O$ be the center, then $\left|P F_{1}\right| \cdot\left|P F_{2}\right|+|O P|^{2}=$ $\qquad$
5. Solution: 25 Let $P\left(x_{0}, y_{0}\right)$ be any point on the ellipse other than the endpoints of the major axis, then $\left|P F_{1}\right|=a+e x_{0},\left|P F_{2}\right|=a-e x$, so $\left|P F_{1}\right| \cdot\left|P F_{2}\right|+|O P|^{2}=a^{2}-e^{2} x_{0}^{2}+x_{0}^{2}+y_{0}^{2}$ $=a^{2}+b^{2}=25$.