#### Answer

Choice D

#### Work Step by Step

Since for any $c\gt0$, $|x|\gt c$ implies $x\gt c \text{ or } x\lt-c$, the given inequality, $
|x-3|\gt5
,$ is equivalent to
\begin{array}{l}\require{cancel}
x-3\gt5
\\\\\text{OR}\\\\
x-3\lt-5
.\end{array}
Hence, $\text{
Choice D
.}$