To simplify this expression, we will first expand each set of parentheses:

(2x - 5)(3x + 4) = 6x^2 + 8x - 15x - 20 = 6x^2 - 7x - 20

(x - 3y)(2y - 5x) = 2xy - 5x^2 - 6xy + 15y = -3xy - 5x^2 + 15y

Now we can multiply the two expanded expressions:

(6x^2 - 7x - 20)(-3xy - 5x^2 + 15y) = -18x^2y + 21xy + 60x^2 - 35x - 45xy + 52x^2 + 150y = 94x^2 - 63xy - 35x + 150y

Next, we will expand the other set of parentheses:

a(a - 5) = a^2 - 5a

Now we can subtract (a - 2)(a - 3) from the previous result:

(a^2 - 5a) - (a^2 - 5a - 6) = a^2 - 5a - a^2 + 5a + 6 = 6

Therefore, the final simplified expression is 94x^2 - 63xy - 35x + 150y + 6.