Answer
$$\left( {0,0,0} \right)$$
Work Step by Step
$$\eqalign{
& z = 5xy \cr
& 5xy - z = 0 \cr
& {\text{Consider}} \cr
& F\left( {x,y,z} \right) = 5xy - z \cr
& {\text{Calculating the partial derivatives}} \cr
& {F_x}\left( {x,y,z} \right) = 5y \cr
& {F_y}\left( {x,y,z} \right) = 5x \cr
& {F_z}\left( {x,y,z} \right) = - 1 \cr
& {\text{Find the gradient }}\nabla F\left( {x,y,z} \right) \cr
& \nabla F\left( {x,y,z} \right) = 5y{\bf{i}} + 5x{\bf{j}} - {\bf{k}} \cr
& {\text{Find the point}}\left( {\text{s}} \right){\text{ on the surface at which the tangent plane }} \cr
& {\text{is horizontal}}. \cr
& 5y = 0 \to y = 0 \cr
& 5x = 0 \to x = 0 \cr
& z = 5xy \cr
& z = \left( 0 \right)\left( 0 \right) \cr
& z = 0 \cr
& {\text{The point is}} \cr
& \left( {0,0,0} \right) \cr} $$