Parallel lines have the same slope, so the slope is -4/5.
We have a point (-5,1) and a slope (-4/5), so let's do point slope form:
y - y1 = m(x - x1)
y - 1 = (-4/5)(x - -5)
y - 1 = (-4/5)(x + 5)
y - 1 = (-4/5)x - 4
y = (-4/5)x - 4 + 1
y = (-4/5)x - 3