Answer
$-3 \le x \le 7$
Work Step by Step
Recall:
$|a| \le b \longrightarrow -b\le a \le b$
Use the rule above with $a=x-2$ and $b=5$ to obtain:
\begin{align*}
|x-2|\le 5 \\
&\longrightarrow -5 \le x-2 \le 5\\
&-5+2 \le x-2+2 \le 5+2\\
&-3 \le x \le 7
\end{align*}