Answer
$(5y-8)(y+4)$
Work Step by Step
Using the factoring of trinomials in the form $ax^2+bx+c,$ the given expression,
\begin{align*}
5y^2+12y-32
\end{align*}
has $ac=
5(-32)=-160
$ and $b=
12
.$
The two numbers with a product of $c$ and a sum of $b$ are $\left\{
-8,20
\right\}.$ Using these $2$ numbers to decompose the middle term of the trinomial expression above results to
\begin{align*}
5y^2-8y+20y-32
\end{align*}
Grouping the first and second terms and the third and fourth terms, the expression above is equivalent to
\begin{align*}
(5y^2-8y)+(20y-32)
\end{align*}
Factoring the $GCF$ in each group results to
\begin{align*}
y(5y-8)+4(5y-8)
\end{align*}
Factoring the $GCF=
(5y-8)
$ of the entire expression above results to
\begin{align*}
(5y-8)(y+4)
\end{align*}