#### Answer

Upon substitution, the given inequality with the given value of the variable ends with a FALSE statement.

#### Work Step by Step

Substituting $x=-7$ in the inequality $|x|\lt5$ results to
\begin{array}{l}\require{cancel}
|x|\lt5
\\\\
|-7|\lt5
\\\\
7\lt5
\text{ (FALSE)}
.\end{array}
Since the substitution above ended with a FALSE statement, then $x=-7$ is not a solution to the inequality.