This looks like tons of fun. I kinda like the "get banned for 5 min" idea, but I think it might hinder player count.
I like the idea too, except 5 minutes is a bit much for the kind of fast-paced game this is. If you're good, you'll get 15 minutes of life at most. On average, probably only 3.
It would be good to allow other players to enter, were the server to become full. Otherwise, the ban time should be lower to maybe just a minute, or just become a kick instead.