The coordinates would be (-5/6, 22/3).
We start by finding the slope of the segment; slope = rise/run:
(9-3)/(-5-10) = 6/-15 = -2/5
Since we want the segment split into a 5:1 ratio, there will be 6 sections. We will add 5/6 of the rise to the y-coordinate and 5/6 of the run to the x-coordinate:
Rise (y): 5/6(-2)+9 = (-10/6) + 9 = (-10/6) + 54/6 = 44/6 = 22/3
Run (x): 5/6(5)+(-5) = 25/6 - 5 = 25/6 - 30/6 = -5/6
