Primary for 5.5-6 gal batches should be in a 6.5 carboy (extra wort volume for sediment loss). Secondary and aging in the 5 if necessary. I have used a 6 gal for primary, and needed a blow off tube to contain the reaction. I like the 6.5 gal best because they are larger diameter cylinder, you will read that commercially, short wide fermenters are preferred to tall skinny ones.
6 gal secondary, yup, done that too. I did my pomegranate wit in a 6 with about 4 inches head space, the pomegranate picked up fermentation and forced out the O2. Even the action of racking to the secondary creates a CO2 blanket on top of your beer. Bigger is better!