Answer
$y=\{ -5,-4\}$
Work Step by Step
Squaring both sides of the inequality and using the properties of radicals, the solution to the given equation is
\begin{array}{l}\require{cancel}\left(
\sqrt{y+5}
\right)^2=\left(
y+5
\right)^2
\\\\
y+5=(y)^2+2(y)(5)+(5)^2
\\\\
y+5=y^2+10y+25
\\\\
0=y^2+(10y-y)+(25-5)
\\\\
y^2+9y+20=0
\\\\
(y+4)(y+5)=0
\\\\
y=\{ -5,-4\}
.\end{array}
Upon checking, both solutions, $
y=\{ -5,-4\}
,$ satisfy the original equation.
