Let's begin by listing out the information given to us:
[tex]\begin{gathered} h\mleft(x\mright)=5x-3 \\ m\mleft(x\mright)=-2x^2 \\ \mleft(h^om\mright)\mleft(x\mright)=5(-2x^2)-3 \\ (h^om)(1)=-10x^2-3=-10(-1^3)-3 \\ (h^om)(1)=10-3=7 \\ (h^om)(1)=7 \end{gathered}[/tex]