After upgrade from v3 to v5, stuck on "update complete" screen and can't access admin areas

I just updated my site from v3.3 to 5.4.3. It went mostly without issue, and I arrived at the “upgrade complete” screen. I can log into the client-facing part of the site and it seems to work correctly.

The issue is that I can’t get to the admin portion of the site. When I go to admin.php, it just shows the “upgrade complete” screen again. The links on that screen, which go to various admin areas, also take me to the “upgrade complete” screen once again.

How can I get out of this cycle and get to the admin areas?