Let's simplify the equation step by step:

Begin by simplifying the left side of the equation:
(4-2x) + (5x-3)
= 4 - 2x + 5x - 3
= 3x + 1

Now simplify the right side of the equation:
(x-2) - (x+3)
= x - 2 - x - 3
= -5

Re-write the equation with the simplified expressions on each side:
3x + 1 = -5

Since the equation doesn't have a solution (3x + 1 cannot equal -5), we conclude that there is no solution to this equation.