1. **State the problem:** We need to find the value of the expression $5b + c^3$ when $b=7$ and $c=4$. 2. **Write the expression:** The expression is $5b + c^3$. 3. **Substitute the values:** Replace $b$ with 7 and $c$ with 4: $$5 \times 7 + 4^3$$ 4. **Calculate powers and multiplication:** $$5 \times 7 = 35$$ $$4^3 = 4 \times 4 \times 4 = 64$$ 5. **Add the results:** $$35 + 64 = 99$$ 6. **Final answer:** The value of the expression is $99$. Therefore, the correct choice is D 99.