1. The problem is to simplify $-331$ modulo $5$. 2. The modulo operation finds the remainder when one number is divided by another. 3. To simplify $-331 \bmod 5$, we find the remainder of $-331$ divided by $5$. 4. First, divide $331$ by $5$: $$331 \div 5 = 66 \text{ remainder } 1$$ 5. Since $-331$ is negative, we use the property: $$a \bmod n = (a + kn) \bmod n$$ for some integer $k$ to make the number positive. 6. Add $5 \times 67 = 335$ to $-331$: $$-331 + 335 = 4$$ 7. Now, $4 \bmod 5 = 4$. 8. Therefore, $-331 \bmod 5 = 4$. Final answer: $4$