Find $5,7,9,11$ and $13$

Use the Divergence Theorem to evaluate ${}_S$vec$(F)*dvec(S).$

$5.$ vec$(F)(x,y,z)=($:$xy{e}^z,x{y}^2{z}^3,-y{e}^z$:$),S$ is the surface of the box bounded by the coordinate planes and the planes $x=3,y=2,z=1.$

$7.$ vec$(F)(x,y,z)=($:$3x{y}^2,x{e}^z,z^3$:$),S$ is the surface of the solid bounded by the cylinder $y^2+z^2=1$ and the planes $x=-1$ and $x=2.$

$9.$ vec$(F)(x,y,z)=($:$x{e}^y,z-e^y,-xy$:$),S$ is the ellipsoid $x^2+2y^2+3z^2=4.$

$11.$ vec$(F)(x,y,z)=($:$2x^3+y^3,y^3+z^3,3y^{2}z$:$),S$ is the surface of the solid bounded by the paraboloid $z=1-x^2-y^2$ and the $xy-$plane.

$13.$ vec$(F)=|vec(r)|vec(r),$ where vec$(r)=($:$x,y,z$:$),S$ consists of the hemisphere $z=\sqrt[\phantom{2}]{1-x^2-y^2}$ and the disk $x^2+y^{2}1$ in the $xy-$plane.