1. **State the problem:** Simplify the expression $(5p^2 - 3) + (2p^2 - 3p^3)$. 2. **Write down the expression:** $$5p^2 - 3 + 2p^2 - 3p^3$$ 3. **Group like terms:** Group the terms with $p^3$, $p^2$, and constants separately: $$-3p^3 + (5p^2 + 2p^2) - 3$$ 4. **Combine like terms:** $$-3p^3 + 7p^2 - 3$$ 5. **Final simplified expression:** $$\boxed{-3p^3 + 7p^2 - 3}$$ This is the simplified form of the given polynomial expression.