To solve the equation (x + 1)(x - 3) = (x - 2)(x - 5), we first need to expand both sides of the equation:

Expanding the left side:
(x + 1)(x - 3)
= x(x) + x(-3) + 1(x) + 1(-3)
= x^2 - 3x + x - 3
= x^2 - 2x - 3

Expanding the right side:
(x - 2)(x - 5)
= x(x) + x(-5) - 2(x) - 2(-5)
= x^2 - 5x - 2x + 10
= x^2 - 7x + 10

Now our equation becomes:
x^2 - 2x - 3 = x^2 - 7x + 10

To solve for x, we can simplify the equation:
x^2 - 2x - 3 = x^2 - 7x + 10
-2x + 7x = 10 + 3
5x = 13
x = 13/5

Therefore, the solution to the equation is x = 13/5.