To translate the figure 5 units to the left and 2 up, apply the following translation to each coordinate of the figure
[tex]T_{(-5,2)}\colon(x,y)\rightarrow(x-5,y+2)[/tex]
So, you have
[tex]\begin{gathered} E(4,-1)\rightarrow E^{\prime}(4-5,-1+2)\rightarrow E^{\prime}(-1,1) \\ F(0,-3)\rightarrow F^{\prime}(0-5,-3+2)\rightarrow F^{\prime}(-5,-1) \\ G(2,-4)\rightarrow G^{\prime}(2-5,-4+2)\rightarrow G^{\prime}(-3,-2) \\ H(6,-2)\rightarrow H^{\prime}(6-5,-2+2)\rightarrow H^{\prime}(1,0) \end{gathered}[/tex]
Therefore, the coordinates of E' are (-1,1) and the correct answer is C. E(-1,1).
