Answer
$x=39$
Work Step by Step
Using the properties of equality, the given equation, $
\sqrt[4]{2x+3}-5=-2
$, is equivalent to
\begin{array}{l}
\sqrt[4]{2x+3}=-2+5
\\\\
\sqrt[4]{2x+3}=3
.\end{array}
Raising both sides to the $\text{
4th
}$ power, the solution to the equation above, $
\sqrt[4]{2x+3}=3
$, is
\begin{array}{l}
2x+3=81
\\\\
2x=81-3
\\\\
2x=78
\\\\
x=39
.\end{array}
Upon checking, $
x=39
$ satisfies the given equation.