Because it was only 9 days after originally testing positive, it's much more likely that it's a Paxlovid rebound than that Biden got reinfected. He only tested positive after completing the 5-day Paxlovid treatment, after which a significant amount of people end up testing positive again.

Given that, I don't know why they don't just make the treatment longer than 5 days. Maybe 5 days makes it easier to meet demand?