1. **State the problem:** Simplify the expression $$\frac{4+5-(3\times 3)+10}{5}+2$$. 2. **Recall the order of operations:** Perform multiplication first, then addition and subtraction inside the numerator, followed by division, and finally addition. 3. **Calculate the multiplication:** $$3 \times 3 = 9$$. 4. **Substitute back into the numerator:** $$4 + 5 - 9 + 10$$. 5. **Simplify the numerator step-by-step:** - $$4 + 5 = 9$$ - $$9 - 9 = 0$$ - $$0 + 10 = 10$$ 6. **Divide the numerator by 5:** $$\frac{10}{5} = 2$$. 7. **Add 2 to the result:** $$2 + 2 = 4$$. **Final answer:** $$4$$