I’m not sure what you mean: the oldest book currently checked out?
If you mean oldest publication date, my library assistants attempted to glean this information by wrestling with the information system, and it turns out to be a much more complicated process than anticipated. IOW: we don’t know. If you mean longest checked out, theoretically, that would be 4 years because faculty and staff can check items out for a year and renew 3 times. If a book hasn’t been returned after its last possible due date, it’s marked “missing,” after a month and is no longer checked out, so the checked-out clock stops. IOW, again, we don’t know. My assistants might not always have all the answers, but at least they’re honest about it!