Evaluate the surface integral ∫∫_S F · dS for the given vector field F and the oriented surface S. In other words, find the flux of F across S. For closed surfaces, use the positive (outward) orientation.

F(x, y, z) = x i + y j + 5 k, S is the boundary of the region enclosed by the cylinder x² + z² = 1 and the planes y = 0 and x + y = 2