Expanding the given expression:

(4x-3y)(4x+3y) - (2x+5y)^2
= 16x^2 - 12xy + 12xy - 9y^2 - (4x)^2 - 2(2x)(5y) - (5y)^2
= 16x^2 - 9y^2 - 16x^2 - 20xy - 25y^2
= -9y^2 - 20xy - 25y^2
= -34y^2 - 20xy

Therefore, the simplified expression is -34y^2 - 20xy.