1. **State the problem:** Simplify the expression $5a^2b + ab^2$ if possible. 2. **Identify common factors:** Both terms have a common factor of $ab$. 3. **Factor out the common term:** $$5a^2b + ab^2 = ab(5a + b)$$ 4. **Explanation:** We look for the greatest common factor (GCF) in each term. Here, $a$ appears at least once in both terms, and $b$ appears once in both terms, so $ab$ is the GCF. 5. **Final answer:** The expression factored is $$ab(5a + b)$$