#### Answer

$x=\left\{ -1-\sqrt{5},-1+\sqrt{5} \right\}$

#### Work Step by Step

The left side of the given equation, $
x^2+2x+1=5
,$ is a perfect square trinomial whose factored form is
\begin{array}{l}\require{cancel}
(x+1)^2=5
.\end{array}
Taking the square root of both sides (the Square Root Property), the solutions to the given equation are
\begin{array}{l}\require{cancel}
x+1=\pm\sqrt{5}
\\\\
x=-1\pm\sqrt{5}
.\end{array}
Hence, $
x=\left\{ -1-\sqrt{5},-1+\sqrt{5} \right\}
.$