#### Answer

$y=-3$

#### Work Step by Step

Raising both sides to the $\text{
4th
}$ power, the given equation, $
(5y+31)^{1/4}=2
$, becomes
\begin{array}{l}
5y+31=16
\\\\
5y=16-31
\\\\
5y=-15
\\\\
y=-\dfrac{15}{5}
\\\\
y=-3
.\end{array}
Upon checking, only $
y=-3
$ satisfies the original equation.