Lines & Planes in Space · Superchallenge problem

Let $A = (p, 0, 0)$, $B = (p + 4, 0, 0)$, $C = (0, q, q + 2)$ and $D = (0, q + 3, q + 5)$, where $p$ and $q$ are any real numbers. Show that the volume of tetrahedron $ABCD$ does not depend on $p$ and $q$, and find it.