10. Given $F_{1}$ and $F_{2}$ are the left and right foci, respectively, of

the hyperbola $C: \frac{x^{2}}{a^{2}}-\frac{y^{2}}{b^{2}}=1(a>0, b>0)$,
the circle with diameter $F_{1} F_{2}$ intersects the hyperbola $C$ at point $P$ in the second quadrant. If the eccentricity of the hyperbola is 5, then the value of $\cos \angle P F_{2} F_{1}$ is ( ).
(A) $\frac{3}{5}$
(B) $\frac{3}{4}$
(C) $\frac{4}{5}$
(D) $\frac{5}{6}$