1. **State the problem:** Simplify the expression $5y + (y-2)(y+8)$.\n\n2. **Recall the formula:** Use the distributive property (FOIL) to expand $(y-2)(y+8)$.\n\n3. **Expand the product:**\n$$ (y-2)(y+8) = y \cdot y + y \cdot 8 - 2 \cdot y - 2 \cdot 8 = y^2 + 8y - 2y - 16 $$\n\n4. **Simplify the terms inside the parentheses:**\n$$ y^2 + (8y - 2y) - 16 = y^2 + 6y - 16 $$\n\n5. **Add the $5y$ term:**\n$$ 5y + y^2 + 6y - 16 $$\n\n6. **Combine like terms:**\n$$ y^2 + (5y + 6y) - 16 = y^2 + 11y - 16 $$\n\n**Final answer:**\n$$ y^2 + 11y - 16 $$