#### Answer

$x=\left\{ -5,5 \right\}$

#### Work Step by Step

Using the properties of equality, the given equation, $
|x|-1=4
,$ is equivalent to
\begin{array}{l}\require{cancel}
|x|=4+1
\\\\
|x|=5
.\end{array}
Since for any $a\gt0$, $|x|=a$ implies $x=a$ OR $x=-a$, then the equation above is equivalent to
\begin{array}{l}\require{cancel}
x=5 \text{ OR }x=-5
.\end{array}
Hence, the solutions are $
x=\left\{ -5,5 \right\}
.$