1. **State the problem:** Simplify the expression $$(2b - 3a)^3 + 8(2a - b)(a - b) - 5a(a - b)^2.$$\n\n2. **Recall formulas and rules:**\n- Cube of a binomial: $(x - y)^3 = x^3 - 3x^2y + 3xy^2 - y^3$.\n- Distributive property: $a(b + c) = ab + ac$.\n- Square of a binomial: $(a - b)^2 = a^2 - 2ab + b^2$.\n\n3. **Expand each term:**\n- Expand $(2b - 3a)^3$ using binomial cube formula with $x=2b$, $y=3a$:\n$$ (2b)^3 - 3(2b)^2(3a) + 3(2b)(3a)^2 - (3a)^3 = 8b^3 - 36b^2a + 54ba^2 - 27a^3.$$\n\n- Expand $8(2a - b)(a - b)$:\nFirst, expand $(2a - b)(a - b)$:\n$$2a \cdot a - 2a \cdot b - b \cdot a + b \cdot b = 2a^2 - 2ab - ab + b^2 = 2a^2 - 3ab + b^2.$$\nMultiply by 8:\n$$8(2a^2 - 3ab + b^2) = 16a^2 - 24ab + 8b^2.$$\n\n- Expand $-5a(a - b)^2$:\nFirst, expand $(a - b)^2$:\n$$a^2 - 2ab + b^2.$$\nMultiply by $-5a$:\n$$-5a(a^2 - 2ab + b^2) = -5a^3 + 10a^2b - 5ab^2.$$\n\n4. **Combine all expanded terms:**\n$$8b^3 - 36b^2a + 54ba^2 - 27a^3 + 16a^2 - 24ab + 8b^2 - 5a^3 + 10a^2b - 5ab^2.$$\n\n5. **Group like terms:**\n- $a^3$ terms: $-27a^3 - 5a^3 = -32a^3$\n- $a^2b$ terms: $54ba^2 + 10a^2b = 64a^2b$\n- $a^2$ term: $16a^2$\n- $ab^2$ term: $-5ab^2$\n- $ab$ term: $-24ab$\n- $b^3$ term: $8b^3$\n- $b^2a$ term: $-36b^2a$ (same as $-36a b^2$)\n- $b^2$ term: $8b^2$\n\nRewrite $-36b^2a$ as $-36ab^2$ to combine with $-5ab^2$:\n$$-36ab^2 - 5ab^2 = -41ab^2.$$\n\n6. **Final simplified expression:**\n$$\boxed{-32a^3 + 64a^2b + 16a^2 - 24ab + 8b^3 + 8b^2 - 41ab^2}.$$