Graph -5<x-4<=1

$- 5 < x - 4 \leq 1$

Add $4$ to each section of the inequality because it does not contain the variable we are trying to solve for.

$- 5 + 4 < x \leq 1 + 4$

Add $- 5$ and $4$ .

$- 1 < x \leq 1 + 4$

Add $1$ and $4$ .

$- 1 < x \leq 5$