1. **State the problem:** Simplify the expression $5(y+4)$. 2. **Formula used:** Use the distributive property of multiplication over addition: $$a(b+c) = ab + ac$$ 3. **Apply the distributive property:** Multiply 5 by each term inside the parentheses: $$5(y+4) = 5 \times y + 5 \times 4$$ 4. **Simplify:** $$5y + 20$$ 5. **Final answer:** The simplified expression is $5y + 20$.