#### Answer

Choice H

#### Work Step by Step

Since for any $c\gt0$, $|x|\lt c$ implies $-c\lt x\lt c$ (or $|x|\le c$ implies $-c\le x\le c$), the given inequality, $
|x-3|\lt5
,$ is equivalent to
\begin{array}{l}\require{cancel}
-5\lt x-3\lt5
.\end{array}
Hence, $\text{
Choice H
.}$