Answer
$(-2,3)$ does not satisfy one of the equations therefore it is not a solution of the system.
Work Step by Step
The given point is a solution of the system if its coordinates satisfy both equations.
$\\\\\\$Substitute the x and y coordinates of (-2, 3) to each equation to have:
$\\\\\begin{array}{r}5x+3y \stackrel{?}{=}-1
\\5(-2)+3(3)\stackrel{?}{=}-1
\\-10+9\stackrel{?}{=}-1
\\-1\stackrel{\checkmark}{=}-1\end{array}$
$\\\\\begin{array}{r}x-y \stackrel{?}{=}1
\\-2-3\stackrel{?}{=}1
\\-5\ne1\end{array}$