Question $11$ Worth $8$ points

Use the Divergence Theorem to calculate the surface integral ${}_{S}F*dS$; that is$,$ calculate the flux of $F$ across $S.F(x,y,z)=xy{e}^{z}i+x{y}^2{z}^{3}j-y{e}^{z}k,S$ is the surface of the box bounded by the coordinate plane and the planes $x=5,y=2,z=1$