Simplify: (5x − 3)(x + 2) − (2x + 5)(4x − 3)

To simplify, we will proceed as follows:

(5x − 3)(x + 2) − (2x + 5)(4x − 3)

$=[(5 x-3)(x+2)]-[(2 x+5)(4 x-3)]$

$=[5 x(x+2)-3(x+2)]-[2 x(4 x-3)+5(4 x-3)]$  (Distributive law)

$=5 x^{2}+10 x-3 x-6-8 x^{2}+6 x-20 x+15$

$=5 x^{2}-8 x^{2}+10 x-3 x+6 x-20 x-6+15$          (Rearranging)

$=5 x^{2}-8 x^{2}+10 x-3 x+6 x-20 x-6+15$          (Combining like terms)

$=-3 x^{2}-7 x+9$

Hence, the answer is $-3 x^{2}-7 x+9$.