#### Answer

x={ -5,5 }

#### Work Step by Step

$\bf{\text{Solution Outline:}}$
To solve the given equation, $
|x|=5
,$ use the definition of an absolute value equality.
$\bf{\text{Solution Details:}}$
Since for any $c\gt0$, $|x|=c$ implies $x=c \text{ or } x=-c,$ the given equation is equivalent to
\begin{array}{l}\require{cancel}
x=5
\\\\\text{OR}\\\\
x=-5
.\end{array}
Hence, $
x=\{ -5,5 \}
.$