Well first, we know BD which is equal to 24 is bisected by QC. Thus BC is 12 units long. Now that we know 2 sides of the triangle PBC, we can find the third missing side, PB, using the Pythagorean Theorem:
BC^2 + PB^2 = PC^2
12^2 + PB^2 = 13^2
144 + PB^2 = 169
PB^2 = 25
PB = 5