Perpendicular lines have slopes that are negative reciprocals of each other, so the equation of the line in point-slope form is:
[tex]y-4=-\frac{5}{2}(x+3)[/tex]
Rewriting this in standard form,
[tex]2y-8=-5(x+3) \\ \\ 2y-8=-5x-15 \\ \\ \boxed{5x+2y=-7}[/tex]
