Answer
$2\frac{2}{3}$
Work Step by Step
Since $x=-1$ and $y=5$, we have
$$
\frac{(y - x)^2 - 4y}{4x^2+2}=\frac{(5- (-1))^2 - 4(5)}{4(-1)^2+2}\\
=\frac{(5+1)^2 -20}{4 +2}=\frac{36-20}{6}\\
=\frac{16}{6}=\frac{8}{3}=2\frac{2}{3}
.$$
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