1. **State the problem:** Multiply out the brackets and simplify the expression $3(3n-2)+5$. 2. **Recall the distributive property:** To multiply a number by a bracket, multiply the number by each term inside the bracket separately. 3. **Apply the distributive property:** $$3(3n-2) = 3 \times 3n - 3 \times 2 = 9n - 6$$ 4. **Add the remaining term:** $$9n - 6 + 5$$ 5. **Simplify by combining like terms:** $$-6 + 5 = -1$$ 6. **Final simplified expression:** $$9n - 1$$ This means the expression $3(3n-2)+5$ simplifies to $9n - 1$.