1. **State the problem:** Simplify the expression $$(-7p - 3) + (p^2 + 5)$$. 2. **Recall the rules:** When adding algebraic expressions, combine like terms. Like terms have the same variable raised to the same power. 3. **Rewrite the expression:** $$-7p - 3 + p^2 + 5$$. 4. **Group like terms:** The terms are $$p^2$$ (quadratic), $$-7p$$ (linear), and constants $$-3$$ and $$5$$. 5. **Combine constants:** $$-3 + 5 = 2$$. 6. **Write the simplified expression:** $$p^2 - 7p + 2$$. **Final answer:** $$p^2 - 7p + 2$$