Find the flux of \( \vec{F}=\left(4 x, 2 y, x^{2}+y^{2}\right) \) across the surface \( (S) \) that is the part of the plane \( z=5 x-2 y-4 \), where \( (x, y) \) belongs to the disk \( x^{2}+y^{2} \leq 2 \). Given that \( (S) \) is oriented upward.
Answer: \( \square \)
