1. **State the problem:** Evaluate the expression $(-10) \div (-2)^2 + 5^3$. 2. **Recall the order of operations:** Use PEMDAS (Parentheses, Exponents, Multiplication/Division (left to right), Addition/Subtraction (left to right)). 3. **Calculate the exponent:** $(-2)^2 = (-2) \times (-2) = 4$. 4. **Perform the division:** $(-10) \div 4 = -2.5$. 5. **Calculate the cube:** $5^3 = 5 \times 5 \times 5 = 125$. 6. **Add the results:** $-2.5 + 125 = 122.5$. **Final answer:** $122.5$