Determine Whether or Not Vector Field Is Conservative $f$ Such That $\mathbf { F } = \nabla f$

Short Answer

Determine whether or not vector field is conservative. If it is conservative, find a function $f$ such that $\mathbf { F } = \nabla f$ .
$$\mathbf { F } ( x , y , z ) = 5 z y \mathbf { i } + 5 x z \mathbf { j } + 5 x y \mathbf { k }$$