To expand the given expression, we will first distribute the terms within the parentheses:

(5x-2)(x+1) = 5x(x) + 5x(1) - 2(x) - 2(1)
= 5x^2 + 5x - 2x - 2
= 5x^2 + 3x - 2

Now, let's expand the second part of the expression:
(5-2x)^2 = (5-2x)(5-2x) = 5(5) - 5(2x) - 2x(5) - 2x(-2x)
= 25 - 10x - 10x + 4x^2
= 4x^2 - 20x + 25

Now, subtract the second expanded expression from the first expanded expression:
(5x-2)(x+1) - (5-2x)^2 = (5x^2 + 3x - 2) - (4x^2 - 20x + 25)
= 5x^2 + 3x - 2 - 4x^2 + 20x - 25
= x^2 + 23x - 27

Therefore, (5x-2)(x+1) - (5-2x)^2 simplifies to x^2 + 23x - 27.