#### Answer

$\color{blue}{\left\{-5-i\sqrt3, -5+i\sqrt3\right\}}$

#### Work Step by Step

RECALL:
If $x^2=a$, then taking the square root of both sides gives $x = \pm \sqrt{a}$.
Take the square root of both sides of the given equation to obtain:
$\sqrt{(x+5)^2}=\pm \sqrt{-3}
\\x+5 =\pm \sqrt{-1(3)}$
Since $\sqrt{-1}=i$, then the expression above is equivalent to:
$x+5=\pm i\sqrt{3}$
Subtract $5$ to both sides:
$x =-5 \pm i\sqrt{3}$
Thus, the solution set is $\color{blue}{\left\{-5-i\sqrt3, -5+i\sqrt3\right\}}$.