I think the majority of barrel users employ the barrel for aging and not primary fermentation. I could be wrong, as I don't have one. Doing the primary ferment in the barrel would simplify things by allowing you to fill the barrel right up to the bung hole and not worry about any blowout that would come along with a krausen. Just one option.
Since a barrel isn't air-tight, I don't think headspace would be too much of a concern. With a smaller barrel (5gal), you're likely to have it aging less time (more surface area imparts more flavor faster), so I don't think exposure to oxygen will be an issue for a shorter amount of time.