Answer
$x=\left\{-2.495, 2.757\right\}$
Refer to the image below for the graph.
Work Step by Step
To solve the given equation graphically, perform the following steps:
(1) Let each side of the equation represent a function then graph each function on the same coordinate plane.
Graph $y=\sqrt{x+4}$ (the blue graph) and $y=x^2-5$ (the red graph).
(refer to the attached image in the answer part above for the graph)
(2) Identify the point/s where the two graphs intersect. The x-coordinate of point of intersection is a solution of the given equation.
The graphs intersect at $(-2.495, 1.227)$ and $(2.757, 2.599)$.
Therefore, the solutions to the given equation are:
$x=\left\{-2.495, 2.757\right\}$
