Parallel lines have the same slope, so the slope is -3/5, because 5y=17-3x, y=-3x/5+17/5.
The equation of the line is y=-3x/5+a where we have to find a by plugging in the given point:
3=6/5+a, so a=9/5 and y=-3x/5+9/5, which can be written 3x+5y=9 to match its parallel counterpart.