jmc

Since line segment $AD$ is perpendicular to the plane of $PAB$, angle $PAD$ is a right angle. In right triangle $PAD,PA=3\text{mbox}andAD=AB=5$. By the Pythagorean Theorem $PD=\sqrt{3^2+5^2}=\boxed{\sqrt{34}}$. The fact that $PB=4$ was not needed.