We have expression [tex]-5 < x - 4 \geq 1[/tex] that renders the system of inequalities,
[tex]
\begin{cases}
-5 < x - 4 \\
x - 4 \geq 1
\end{cases}
[/tex]
Which can be simplified to,
[tex]
\begin{cases}
x > -1 \\
x \geq 5
\end{cases}
[/tex]
So what we get is something greater than -1 and at the same time greater or equal to 5, so the solution is,
[tex]x\in(\infty,-1)\cap(\infty, 5]=\boxed{(\infty,5]}[/tex].
Hope this helps.
