Find the Flux of the Vector Field F Across the Surface

Multiple Choice

Find the flux of the vector field F across the surface S in the indicated direction.
- $\mathbf { F } = 5 x \mathbf { i } + 5 y \mathbf { j } + \mathrm { z } ^ { 2 } \mathbf { k } ; \mathrm { S }$ is portion of the cylinder $\mathrm { x } ^ { 2 } + \mathrm { y } ^ { 2 } = 25$ between $\mathrm { z } = 0$ and $\mathrm { z } = 5$ ; direction is outward

A) 625
B) 1250
C) $- 1250 \pi$
D) $1250 \pi$