1. **Problem statement:** Simplify the expression $-4^5 + 11 \cdot 4^5$. 2. **Recall the distributive property:** For terms with the same base and exponent, $a \cdot x^n + b \cdot x^n = (a+b) \cdot x^n$. 3. **Apply the property:** $$-4^5 + 11 \cdot 4^5 = (-1) \cdot 4^5 + 11 \cdot 4^5 = (-1 + 11) \cdot 4^5$$ 4. **Simplify the coefficients:** $$(-1 + 11) = 10$$ 5. **Final simplified expression:** $$10 \cdot 4^5$$ **Answer:** $10 \cdot 4^5$