jmc

We write $555$ in powers of $5$. The largest power of $5$ which is smaller than $555$ is $5^3=125$, and the greatest multiple of $125$ which is less than $555$ is $4$. We get that $555-4\cdot 125=55$. The largest power of $5$ that is less than $55$ is $5^2=25$, and the greatest multiple of $25$ less than $55$ is $2$. We get $55-2\cdot 25=5$, which is $5^1$. Therefore, we can write $555$ as $4\cdot 5^3+2\cdot 5^2+1\cdot 5^1$. Thus, the answer is $\boxed{4210_5}$.