They close at 5pm but what if there’s still a long wait list by 5? Do they turn all those people away?

Yes , as a rule. Closing time is closing time!

Get there early. Yes they will turn you away they are very busy

If you get there earlier, and are already on the list, you'll be safe. If, say, at 4, they see there are way too many people, they'll stop "new arrivals" from signing in. However, if you are already on the list before that time, and it's after 5 and they still haven't seen you (your pet), they will still see you. They are amazingly fair and amazing prople.