Subtract 4321 base five minus 4232 base five.

We need to subtract $1 - 2$. Since $1 < 2$, we borrow from the next column to the left.
Borrow 1 from the '2' in the $5^1$ place, which means we add 5 to the '1' in the $5^0$ place.
So, 1 becomes $1 + 5 = 6$. The '2' in the $5^1$ place becomes '1'.
Now, we calculate $6 - 2 = 4$.

$$\begin{array}{c} \phantom{0}43\cancel{2}^1\cancel{1}^6_{\text{five}} \\ -\phantom{0}4232_{\text{five}} \\ \hline \phantom{0000}4_{\text{five}} \end{array}$$

We now have '1' in this column (from the original '2' after borrowing).
We need to subtract $1 - 3$. Since $1 < 3$, we borrow from the next column to the left.
Borrow 1 from the '3' in the $5^2$ place, which means we add 5 to the '1' in the $5^1$ place.
So, 1 becomes $1 + 5 = 6$. The '3' in the $5^2$ place becomes '2'.
Now, we calculate $6 - 3 = 3$.

$$\begin{array}{c} \phantom{0}4\cancel{3}^2\cancel{2}^6\cancel{1}^6_{\text{five}} \\ -\phantom{0}4232_{\text{five}} \\ \hline \phantom{000}34_{\text{five}} \end{array}$$

We now have '2' in this column (from the original '3' after borrowing).
We need to subtract $2 - 2 = 0$.

$$\begin{array}{c} \phantom{0}4\cancel{3}^2\cancel{2}^6\cancel{1}^6_{\text{five}} \\ -\phantom{0}4232_{\text{five}} \\ \hline \phantom{00}034_{\text{five}} \end{array}$$

We have '4' in this column.
We need to subtract $4 - 4 = 0$.

$$\begin{array}{c} \phantom{0}4\cancel{3}^2\cancel{2}^6\cancel{1}^6_{\text{five}} \\ -\phantom{0}4232_{\text{five}} \\ \hline 0034_{\text{five}} \end{array}$$

Leading zeros are not typically written, so $0034_{\text{five}}$ is simply $34_{\text{five}}$.

The final answer is $34_{\text{five}}$.