1. **State the problem:** We need to find the polynomial that represents the area of a rectangle whose length is 5 inches longer than its width. 2. **Define variables:** Let the width be $x$ inches. 3. **Express length:** Since the length is 5 inches longer than the width, length $= x + 5$. 4. **Formula for area of a rectangle:** $$\text{Area} = \text{length} \times \text{width}$$ 5. **Substitute values:** $$\text{Area} = (x + 5) \times x$$ 6. **Multiply:** $$\text{Area} = x(x + 5) = x^2 + 5x$$ 7. **Interpretation:** The polynomial representing the area is $x^2 + 5x$. 8. **Compare with options:** Option d) $x^2 + 5x$ matches our result. **Final answer:** The polynomial representing the area is $x^2 + 5x$ (option d).