9. Given $F_{1}, F_{2}$ are the left and right foci of the hyperbola $C: \frac{x^{2}}{a^{2}}-\frac{y^{2}}{b^{2}}=1(a>0, b>0)$, and the circle with $F_{1} F_{2}$ as its diameter intersects the hyperbola $C$ at point $P$ in the second quadrant. If the eccentricity of the hyperbola is 5, then $\cos \angle P F_{2} F_{1}$ equals
A. $\frac{3}{5}$
B. $\frac{3}{4}$
C. $\frac{4}{5}$
D. $\frac{5}{6}$
Let $\left|P F_{2}\right|=x,\left|P F_{1}\right|=y$, from $e=\frac{c}{a}=5 \Rightarrow c=5 a \Rightarrow\left|F_{1} F_{2}\right|=10 a$, then $\left\{\begin{array}{l}x^{2}+y^{2}=100 a^{2}, \\ x-y=2 a\end{array} \Rightarrow\left\{\begin{array}{l}x=8 a, \\ y=6 a\end{array} \Rightarrow \cos \angle P F_{2} F_{1}=\frac{4}{5}\right.\right.$, so the answer is $C$.