\[\left| |x + 5| + 3 \right| = 7\]
\[|x + 5| + 3 = 7\]
\[|x + 5| = 4\]
\[|x + 5| + 3 = - 7\]
\[|x + 5| = - 10 \Longrightarrow нет\ решения.\]
\[Ответ:\ - 1;\ - 9.\]