5. In the rectangular prism $A B C D-E F G H$ shown in the figure, let $P$ be the center of rectangle $E F G H$, and line segment $A P$ intersects plane $B D E$ at point $Q$. If $A B=3, A D=2, A E=$ 1, then $P Q=$ $\qquad$.
(5) $\frac{\sqrt{17}}{4}$