5. If the edges $AB, BC$ of the quadrilateral pyramid $P-ABCD$ are both $\sqrt{2}$, and the lengths of the other edges are all 1, then the volume of the quadrilateral pyramid is $\qquad$ .
Given, construct $P O \perp$ plane $A B C D$, since $P A=$ $P B=P C=P D \Rightarrow O A=O B=O C=$ $O D \Rightarrow \angle B A D=\angle B C D=90^{\circ}$, thus $O$ is the midpoint of $B D$. From the above, $B D=\sqrt{3}$ $\Rightarrow P O=\frac{1}{2}, S_{A B C D}=\sqrt{2}$, so the volume of the quadrilateral pyramid is $V=\frac{\sqrt{2}}{6}$.