Answer
The solutions are:
$x\approx -2.495$ and $x\approx 2.757$.
Work Step by Step
To solve the given equation graphically, do the following steps:
(1) Use a graphing utility to graph $y=\sqrt{x+4}$ (refer to the red graph) and $y=x^2-5$ (refer to the blue graph);
(2) Identify the points where the graphs intersect each other. The x-coordinates of these points are the solutions to the given equation.
Thus, the approximate solutions are $x=-2.495$ and $x=2.757$.
(refer to the attached image below for the graph)