1. **State the problem:** Simplify the expression $$-5^2 + (-5)^2$$. 2. **Recall the order of operations and exponent rules:** - Exponentiation is done before negation. - $$-5^2$$ means the negative of $$5^2$$, so $$-5^2 = -(5^2)$$. - $$(-5)^2$$ means $$-5$$ multiplied by itself, so $$(-5)^2 = (-5) \times (-5)$$. 3. **Calculate each term:** - $$5^2 = 25$$. - So, $$-5^2 = -25$$. - $$(-5)^2 = 25$$ because a negative times a negative is positive. 4. **Add the results:** $$-25 + 25 = 0$$. **Final answer:** $$0$$