Let (x1, y1) and (x2, y2) be the co-ordinates of the points P and Q and let the point R (x, y) divides the line-segment PQ internally in a given ratio m : n (say), i.e., PR : RQ = m : n then:

x = (m*x2 + n*x1)/(m + n)

y = (m*y2 + n*y1)/(m + n)

In our case we have P(2, -5) and Q(-3, 5) that is x1 = 2, y1 = -5, x2 = -3, y2 = 5 and PR : RQ = 2 : 3 that is

m = 2 and n = 3. Now we plug the values in the formulas:

x = (2*(-3) + 3*2)/(2 + 3)

x = 0

y = (2*5 + 3*(-5))/(2 + 3)

y = - 5/5

y = - 1

The coordinates of the point are (0, -1)

Or if we plot the points we can see that (0, -1) is 3/5 of the way from (2, -5) to (-3, 5).