What is 4234 base 5 minus 44 base 5?

We have $4 - 4 = 0$.

$$\begin{array}{c} \phantom{0}4234_{\text{five}} \\ -\phantom{00}44_{\text{five}} \\ \hline \phantom{000}0_{\text{five}} \end{array}$$

We need to subtract $3 - 4$. Since $3 < 4$, we need to borrow from the next column to the left.
Borrow 1 from the '2' in the $5^2$ place, which means we add 5 to the '3' in the $5^1$ place.
So, 3 becomes $3 + 5 = 8$. The '2' in the $5^2$ place becomes '1'.
Now, we calculate $8 - 4 = 4$.

$$\begin{array}{c} \phantom{0}4\cancel{2}^1\cancel{3}^84_{\text{five}} \\ -\phantom{00}44_{\text{five}} \\ \hline \phantom{00}40_{\text{five}} \end{array}$$

We now have '1' in this column (because we borrowed from the original '2').
We need to subtract $1 - 0 = 1$.

$$\begin{array}{c} \phantom{0}4\cancel{2}^1\cancel{3}^84_{\text{five}} \\ -\phantom{00}44_{\text{five}} \\ \hline \phantom{0}140_{\text{five}} \end{array}$$

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

$$\begin{array}{c} \phantom{0}4\cancel{2}^1\cancel{3}^84_{\text{five}} \\ -\phantom{00}44_{\text{five}} \\ \hline 4140_{\text{five}} \end{array}$$

The final answer is $4140_{\text{five}}$.