I would think it depends how long you are going to leave it in there. I ferment 1.5 gallon batches in 6 gallon fermentors quite a bit but only leave it in there for 4 weeks tops.
My guess is that it should be fine for a primary. I am not sure at what point the amount of headspace becomes an issue though, 5at does seem like a good amount of extra space.
I am not one to secondary much, but if it was going to be more than a month after brewday, I would put it in 2 5 gallon carboys. But for up to a month, do you think it will be ok?
For primary, assuming you're using an airlock, should be no problem. I routinely ferment 10 gallons in a 14.3 gal conical for a month. I have no opinion on secondary since I rarely do a secondary. When I do, it's usually a 5 gal batch of something heavy that can stand a bit of oxidation (though I usually don't get any), and I use a 5 gal carboy for those.
I use an 8 gallon fermenter for 4-5 gallons with no issues, but I don't leave it in there more than a few weeks. Also I make sure to open it only once for dry hopping and just barely crack the lid at that time.
If it's your primary vessel, no worries. The oxygen in the head space will get used when the yeast is beginning its work, and the CO2 will create a protective layer in there when the yeast really gets cranking along. Just keep your airlock hydrated. It can dry out over extended conditioning. I have fermented and conditioned in the same vessel with significant head space for over 2 months, and it's one of my best beers so far. It was a Belgian dark, for reference. It even carbonated well after clarifying very nicely in there. 10.6% ABV.
Just as a primary,no problem at all. Much beer is brewed commercially in open tanks (see the Sam Smiths website) and you can't get more headspace than that
