\(\left| {x + 5} \right| = 0.\)
Уравнение вида \(\left| {f\left( x \right)} \right| = a\), где \(a \ge 0\), равносильно совокупности: \(\left[ {\begin{array}{*{20}{c}}{f\left( x \right) = a,\,\,\,}\\{f\left( x \right) = -a.}\end{array}} \right.\)
\(\left| {x + 5} \right| = 0\,\,\,\,\,\,\, \Leftrightarrow \,\,\,\,\,\,\,x + 5 = 0\,\,\,\,\,\,\, \Leftrightarrow \,\,\,\,\,\,\,x = -5.\)
Ответ: \(-5.\)