Solution:

\(\displaystyle{\left|{x}-{5}\right|}{<}{9}\)

set up compound inequality by removing the absolute value

\(\displaystyle-{9}{<}{x}-{5}{<}{9}\)

adding 5 throughout the inequality

\(\displaystyle{5}-{9}{<}{x}-{5}+{5}{<}{9}+{5}\)

\(\displaystyle-{4}{<}{x}{<}{13}\)

\(\displaystyle\therefore{x}\in{\left(-{4},{13}\right)}\)