1. **State the problem:** Expand and simplify the expression $5x(x+1)$. 2. **Formula used:** Use the distributive property $a(b+c) = ab + ac$. 3. **Apply the distributive property:** Multiply $5x$ by each term inside the parentheses: $$5x \times x + 5x \times 1$$ 4. **Simplify each term:** $$5x^2 + 5x$$ 5. **Final answer:** The expanded and simplified form of $5x(x+1)$ is $$5x^2 + 5x$$