Define fluently however you like.
My maximum is 5. I know someone who grew up trilingual (and still retained the use of all three languages as an adult). He became fluent in a fourth language by living for many years as an adult in a country where it was spoken. Then he moved to a country which spoke a fifth language, and was forced to learn that. He managed to become quite fluent, but was always complaining about it, and ended up moving back to a country speaking one of his other four languages.
I also know quite a few people who are "unwillingly" fluent in four languages. But I'm sure the record is much higher than four or five!