Is it possible for AB = 10, BC = 2x + 5 and AC = 5x, given that point B is the midpoint?

If you are talking about lengths of a line segment ABC, with B the midpoint, then

AB + BC = AC

15 + 2x = 5x

3x = 15

x = 3.

But also we must have

AB = BC for B to be a midpoint

10 = 2x + 5

x = 2

So no solution is possible.