Let's simplify the equation step by step:

(3x + 4)(4x - 3) - 5 = (2x + 5)(6x - 7)

Expand the left side of the equation:

12x^2 - 9x + 16x - 12 - 5 = (2x + 5)(6x - 7)

Combine like terms:

12x^2 + 7x - 17 = (2x + 5)(6x - 7)

Expand the right side of the equation:

12x^2 - 14x + 30x - 35 = 12x^2 - 14x + 30x - 35

Combine like terms:

12x^2 + 16x - 35 = 12x^2 + 16x - 35

Since the left side of the equation is equal to the right side after simplification, the equation is true for all values of x. The given equation is verified.