Let's begin by identifying key information given to us:
[tex]\begin{gathered} -4x+5=13 \\ \text{Add ''4x'' to both sides, we have:} \\ -4x+4x+5=13+4x \\ 5=13+4x \\ \text{Subtract ''13'' from both sides, we have:} \\ 5-13=13-13+4x \\ -8=4x\Rightarrow4x=-8 \\ 4x=-8 \\ x=-\frac{8}{4}=-2 \\ x=-2 \end{gathered}[/tex]