Rectangle $ABCD$ is the base of pyramid $PABCD$. If $AB = 3$, $BC = 2$, $\overline{PA}\perp \overline{AD}$, $\overline{PA}\perp \overline{AB}$, and $PC = 5$, then what is the volume of $PABCD$?
[asy]
import three;
triple A = (4,8,0);
triple B= (4,0,0);
triple C = (0,0,0);
triple D = (0,8,0);
triple P = (4,8,6);
draw(B--P--D--A--B);
draw(A--P);
draw(A--C--P, dashed);
draw(B--C--D,dashed);
label("$A$",A,S);
label("$B$",B,W);
label("$C$",C,S);
label("$D$",D,E);
label("$P$",P,N);
[/asy]

Since $\overline{PA}$ is perpendicular to both $\overline{AB}$ and $\overline{AD}$, the segment $\overline{PA}$ is the altitude from the apex to the base of the pyramid.   Applying the Pythagorean Theorem to triangle $ABC$ gives us $AC = \sqrt{13}$.  Applying the Pythagorean Theorem to triangle $PAC$ gives us $PA = \sqrt{PC^2 - AC^2} = \sqrt{12} = 2\sqrt{3}$.

The area of the base of the pyramid is $[ABCD] = (AB)(BC) = 6$, so the volume of the pyramid is $\frac13(6)(2\sqrt{3}) = 4\sqrt{3}$ cubic units.