I have 14 Gallon glass vessels... I brew 10 gallon batches in them... . but when I started I was brewing 5 gallon batches in them... so almost 60% of the vessel was airspace, and I still never had oxygen issues.. the beer produces so much CO2 that at the least, it creates a protective layer...
brewing 5 gallon in 6 gallon container can be done, but you're low on headspace, better rig up a blow-off tube otherwise you might have a mess on your hands