1. **State the problem:** Evaluate the expression $5 \cdot (-3) + ((-2)^3 - 2)^2$. 2. **Recall the order of operations:** We first calculate powers, then multiplication, then addition. 3. **Calculate the first part:** $$5 \cdot (-3) = -15$$ 4. **Calculate the power inside the second part:** $$(-2)^3 = -8$$ 5. **Subtract 2 from the result:** $$-8 - 2 = -10$$ 6. **Square the result:** $$(-10)^2 = 100$$ 7. **Add the two parts together:** $$-15 + 100 = 85$$ **Final answer:** $85$