5. The 3 vertices of a triangle have coordinates $P(-8,5), Q(-15,-19), R(1,-7)$, and the equation of the angle bisector of $\angle P$ can be written as $a x+b y+c=0$, where $a, b, c \in \mathbf{Z}^{+}$ and $(a, b, c)=1$. Then $a+c$ is ( ).
A. 79
B. 89
C. 99
J. 109
5. B

Let the angle bisector of $\angle P$ intersect $P Q$ at $D$, then $\frac{R D}{D Q}=\frac{P R}{R Q}=\frac{15}{25}=\frac{3}{5}$, so the coordinates of point $D$ are $\left(-5,-\frac{23}{2}\right)$, and the equation of $P D$ is $y-5=-\frac{11}{2}(x+8)$, which simplifies to $11 x+2 y+78=0$, so $a+c=89$, hence the answer is B.