2024 AMC 10B Problem 17

In a race among 5 snails, there is at most one tie, but that tie can involve any number of snails. For example, the result of the race might be that Dazzler is first; Abby, Cyrus, and Elroy are tied for second; and Bruna is fifth. How many different results of the race are possible?

\textbf{(A)} 180 \qquad \textbf{(B)} 361 \qquad \textbf{(C)} 420 \qquad \textbf{(D)} 431 \qquad \textbf{(E)} 720

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.