2023 AMC 8 Problem 22

In a sequence of positive integers, each term after the second is the product of the previous two terms. The sixth term in the sequence is 4000. What is the first term?

\textbf{(A)} 1 \qquad \textbf{(B)} 2 \qquad \textbf{(C)} 4 \qquad \textbf{(D)} 5 \qquad \textbf{(E)} 10

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