Answer
The graphs are not perpendicular.
Work Step by Step
RECALL:
(1) In the slope-intercept form of a line's equation $y=mx+b$, $m$=slope and $b$ is the y-coordinate of the y-intercept.
(2) Perpendicular lines have slopes whose product is $-1$ (or negative reciprocals of each other).
Write both equations in slope-intercept form to obtain:
First Equation:
$2x-5y=-3
2x-5y+5y+3=-3+5y+3
\\2x+3=5y
\\\frac{2x+3}{5}=\frac{5y}{5}
\\\frac{2}{5}x+\frac{3}{5}=y
\\y=\frac{2}{5}x+\frac{3}{5}$
Second Equation:
$2x+5y=4
\\2x+5y-2x=4-2x
\\5y=4-2x
\\5y=-2x+4
\\\frac{5y}{5}=\frac{-2x+4}{5}
\\y=-\frac{2}{5}x+\frac{4}{5}$
Note that equations have the slopes $\frac{2}{5}$ and $-\frac{2}{5}$.
Since $\frac{2}{5} \cdot (-\frac{2}{5}) \ne -1$, then the graphs of the two equations are NOT perpendicular lines.