Parameterize the square (call it S) by
[tex]\mathbf s(u,v)=2u\,\mathbf x+2v\,\mathbf z[/tex]
with both [tex]u\in[0,1][/tex] and [tex]v\in[0,1][/tex].
Take the normal vector pointing in the positive y direction to be
[tex]\dfrac{\partial\mathbf s}{\partial v}\times\dfrac{\partial\mathbf s}{\partial u}=4\,\mathbf y[/tex]
Then the current is
[tex]\displaystyle\iint_S(y^2+5)\,\mathbf y\cdot4\,\mathbf y\,\mathrm dA=20\int_0^1\int_0^1\mathrm dA=\boxed{20\,\mathrm A}[/tex]
where [tex]y^2+5[/tex] reduces to just 5 because [tex]y=0[/tex] for all points in S.
