Angle Bisectors of a Triangle Meet

Donald has a triangle $ABC$ with side lengths $AB = 5$, $AC = 6$, and $BC = 7$. He intersects the angle bisectors of $\angle A$ and $\angle B$ to get a point $P$, and he intersects the angle bisectors of $\angle B$ and $\angle C$ to get a point $Q$. What is the distance between points $P$ and $Q$?