Answer
$(x-1)(5x+3)$
Work Step by Step
The two numbers whos product is $
5(-3)=-15
$ and whose sum is $
-2
$ are $\{
-5,3
\}$. Using these numbers to decompose the middle term of the trinomial results to
\begin{array}{l}
5x^2-2x-3
\\=
5x^2-5x+3x-3
\\=
(5x^2-5x)+(3x-3)
\\=
5x(x-1)+3(x-1)
\\=
(x-1)(5x+3)
.\end{array}
