Let:
[tex]\begin{gathered} A=(-5,4) \\ A^{\prime}=(-5,-3) \\ A^{\doubleprime}=(1,3) \end{gathered}[/tex]From A to A' we have a translation 1 unit down and a reflection across the x-axis, so:
[tex]A\to(x,-(y-1))=(-5,-(4-1))=(-5,-3)[/tex]Now, from A' to A'' we have a rotation 180 clockwise, and then a translation 4 units to the left:
[tex]A^{\prime}_{}\to(-x-4,-y)=(-(-5)-4,-(-3))=(1,3)[/tex]Therefore:
[tex]A\to(x,-(y-1)\to A^{\prime}_{}\to(-x-4,-y)\to A^{\doubleprime}[/tex]