1. **State the problem:** Subtract the base five numbers $314_5$ and $233_5$. 2. **Recall the subtraction rules in base five:** In base five, digits range from 0 to 4. If a digit in the minuend is smaller than the corresponding digit in the subtrahend, we borrow 1 from the next higher place value, which equals 5 in the current place. 3. **Write the numbers aligned by place value:** \begin{array}{c c c} &3 & 1 & 4_5 \\ -&2 & 3 & 3_5 \\ \hline \end{array} 4. **Subtract the rightmost digits:** $4 - 3 = 1$ (no borrowing needed). 5. **Subtract the middle digits:** $1 - 3$ is not possible without borrowing. Borrow 1 from the leftmost digit (3 becomes 2), and add 5 to the middle digit: $1 + 5 = 6$. Now subtract: $6 - 3 = 3$. 6. **Subtract the leftmost digits:** After borrowing, leftmost digit is $2 - 2 = 0$. 7. **Combine the results:** The difference is $0 3 1_5$. 8. **Remove leading zeros:** The leading zero can be omitted, so the final answer is $31_5$. **Final answer:** $314_5 - 233_5 = 31_5$.