1. **State the problem:** Simplify the expression $$(2x^5 - 5x^2 + 3) + (5x^3 + 5x^2)$$. 2. **Formula and rules:** When adding polynomials, combine like terms. Like terms have the same variable raised to the same power. 3. **Combine like terms:** - The term $2x^5$ has no like term in the second polynomial, so it stays as is. - Combine $-5x^2$ and $5x^2$: $$-5x^2 + 5x^2 = \cancel{-5x^2} + \cancel{5x^2} = 0$$ - The term $3$ has no like term, so it stays as is. - The term $5x^3$ has no like term in the first polynomial, so it stays as is. 4. **Write the simplified expression:** $$2x^5 + 5x^3 + 3$$ 5. **Final answer:** The simplified polynomial is **$2x^5 + 5x^3 + 3$**.