Answer
approximately $\color{blue}{-1.433}$
Work Step by Step
To approximate the solution to the given equation, treat the expressions on each side of the equation as a function then graph them on the same coordinate plane.
Using a graphing utility, graph the following functions on the same coordinate plane:
$y_1=x^3$ and $y_2=x^2-5$
(refer to the attached image below for the graph)
Notice that the two graphs intersect at the point $(-1.433, -2.945)$.
The solution to the given equation is the $x$-coordinate of the point of intersection of the graphs.
Therefore, the solution to the given equation is approximately $\color{blue}{-1.433}$.
