Given that $\vec{F}(x, y, z)=\sin (y) \hat{x}+\cos (x) \hat{y}+5 \hat{z}$, the integral $\oint \oint _{S} \vec{F}(x, y, z) \cdot \overrightarrow{d s}$ over the unit sphere $S$ centered at the origin evaluates to $\_\_\_\_$
(Round off to one decimal place)
