jmc

We may carry out long division in base 5 just as in base 10. We have $$\begin{array}{cccc}\text{multicolumn}2r2& 0& 4& \\ \text{cline}2-42& 4& 1& 3\\ \text{multicolumn}2r4& \downarrow & & \\ \text{cline}2-2\text{multicolumn}2r0& 1& & \\ \text{multicolumn}2r& 0& \downarrow & \\ \text{cline}3-3\text{multicolumn}2r& 1& 3& \\ \text{multicolumn}2r& 1& 3& \\ \text{cline}3-4\text{multicolumn}2r& & 0& \end{array}$$for a quotient of $\boxed{204_5}$. Note that in the above calculation we have used that $13_5$ divided by $2_5$ is $4_5$, which follows from $4_5\times 2_5=8_{10}=13_5$.