1. **State the problem:** Simplify the expression $$\left[\left(\frac{(-5)(-8) - (4)(5)}{8 - (-2)}\right)^{2}\right]^{3}$$. 2. **Recall the exponent rule:** When you have a power raised to another power, multiply the exponents: $$\left(a^{m}\right)^{n} = a^{mn}$$. 3. **Calculate the numerator:** $$(-5)(-8) - (4)(5) = 40 - 20 = 20$$. 4. **Calculate the denominator:** $$8 - (-2) = 8 + 2 = 10$$. 5. **Form the fraction:** $$\frac{20}{10}$$. 6. **Simplify the fraction:** $$\frac{\cancel{20}}{\cancel{10}} = 2$$. 7. **Apply the exponent inside the bracket:** $$\left(2\right)^{2} = 4$$. 8. **Apply the outer exponent:** $$4^{3} = 64$$. **Final answer:** $$64$$.