Let's first expand the given expression:

(х-5)(2х+3) - (х+4)(4-х)
= 2х^2 + 3х - 10х - 15 - (4х - х^2 + 16 - 4х)
= 2х^2 + 3х - 10х - 15 - 4х + х^2 - 16 + 4х
= 2х^2 + 3х - 10х - 15 - 4х + х^2 - 16 + 4х
= 2х^2 + 3х - 10х - 15 - 4х + х^2 - 16 + 4х
= 2х^2 + 0 - 15 - 16
= 2х^2 - 31

Now, let's simplify the final expression:

2х^2 - 31 = 2х + 5
2х^2 - 2х - 36 = 0
(2х - 9)(х + 4) = 0

Therefore, the solutions are:
х = 9/2, -4