i have used homer buckets, kitty litter buckets, local donuts shop frosting buckets, etc. with plenty of holes drilled both in the bottom and along the bottom sides, i have used the reusable fabric grow bags (root pouch brand) and i have used the cheap PVC grow bags they sell at the hydro stores.
i have found that free is free, and if i can get buckets for free, well i might as well put em to use. That being said, if you don't mind spending a little and having that plastic to throw away at the end of the year, those cheap PVC grow bags work just fine.
(i don't want to throw away 150 more plastic bags each year)
as for the 5 gallons, depends on which peppers your growing. i've had some that did significantly better in 7 or 10 gal bags then the previous year in 5 gal, and other peppers that would have been just fine in 3 gal
the root pouchs hold up great, are certainly reusable, drain well (too well) depending on where your at you might find yourself watering root pouchs more frequently then those PVC grow bags
i think the variation you see in many grows is more due to whats available, rather than whats "better"
but that could be just me. Anyway, buckets or bags, both work fine.
hope this was of some help