The perpendicular equation is y = -5/3x + 20.
You can find this by first realizing that perpendicular lines have opposite and reciprocal slopes. So since it starts at 3/5 we flip it and make it a negative and the new slope is -5/3. Now we can use that and the point to get the y intercept using slope intercept form.
y = mx + b
-5 = (-5/3)(15) + b
-5 = 25 + b
20 = b
And now we can use our new slope and new intercept to model the equation.
y = -5/3x + 20