1. **State the problem:** Evaluate the expression $$[(-3)(4) + 5(-3)][4(-5) - 5(-3)]^2$$. 2. **Apply multiplication inside the brackets:** $$(-3)(4) = -12$$ $$5(-3) = -15$$ So, the first bracket becomes: $$-12 + (-15) = -27$$ 3. **Calculate the second bracket:** $$4(-5) = -20$$ $$-5(-3) = 15$$ So, the second bracket becomes: $$-20 - 15 = -35$$ 4. **Square the second bracket:** $$(-35)^2 = 1225$$ 5. **Multiply the results of the two brackets:** $$-27 \times 1225 = -33075$$ 6. **Final answer:** $$\boxed{-33075}$$