jmc

The given equations are equivalent, respectively, to $$3^a=3^{4(b+2)}\text{and}{5}^{3b}=5^{a-3}.$$ Therefore $a=4(b+2)$ and $3b=a-3$. The solution of this system is $a=-12$ and $b=-5$, so $ab=\boxed{60}$.