Answer
$x=\{ -16,6 \}$
Work Step by Step
Taking the square root of both sides (the Square Root Property), the solutions to the given equation, $
(x+5)^2=121
,$ are
\begin{array}{l}\require{cancel}
(x+5)=\pm\sqrt{121}
\\\\
x+5=\pm\sqrt{(11)^2}
\\\\
x+5=\pm11
\\\\
x=-5\pm11
.\end{array}
Hence, $
x=\{ -16,6 \}
.$