I disagree with the consensus. I've made several 5 gallon batches in a 7 1/2 gallon pot. You don't really need a 15 gallon pot to make a 5 gallon batch. Maybe for a 10 gallon batch....:rockin:
This isn't about need, but rather what would be optimal. Pretty much everyone who has opined in this thread, myself included, has stated in some way or another that a smaller kettle will get the job done. I made do brewing 3.5-5.0G batches with an 8G kettle for nearly 3 years. It worked, but was inconvenient at times, not so much with the smaller batch sizes, as it was perfect for that, but the 5G batches could be pushing the limits when doing larger OG brews and 90 min boils. I was frequently starting boils 1/2" from the top, which was a little bit unnerving. Thank goodness for Fermcap.
Things to consider when upgrading your kettle:
Do you brew big beers? Requires more mash volume.
Do you ever plan to brew lagers or recipes that use Pilsner malt? A 90 min boil is recommended when brewing with Pilsner malt. I'd say 75% of what I brew gets a 90 min boil.
Do you plan to brew big beers that require an extended boil (E.g., Belgian Quad or Wee Heavy)? Requires lots of grain and water.
Would you ever brew a batch in which you might want to keg 5 gallons and bottle age 2 or 3 more? That would be a ~9G batch. I never thought I'd do this, but since I now have a kettle that is sufficiently sized, I've done it a few times now.
Of course, all of the above can be overcome even when using a smaller kettle. A bit of malt extract or sugar can boost gravity without adding much to volume, you can add top-off water to the fermenter, you can do multiple mashes and boils to reach a desired batch size, or even reduce your batch size if you don't want/need 5 gallons of that 1.100 Wee Heavy. In the end, it comes down to what is doable, what is optimal, and how much hassle or compromise you are willing to deal with to get there. There are probably about as many ways to skin this cat as there are cats.
So, a 7.5G kettle will work, but full-volume mashes and/or extended boils will be problematic and require some sort of compromise for a 5.5G batch. A 10G kettle will be better, but will also have limitations under the right conditions. 12G will almost always get the job done and will only be too small under extreme circumstances. A 15G kettle will pretty much handle every scenario wrt to 5.5-6.0G batch size and could easily accommodate most recipes up to 8 or 9G, as well as some 10G brews.
I have a 15G kettle and brew 6G as my standard batch size. As stated above, most batches get a 90 minute boil. This means I start my brew day with ~9G of water in the kettle, which gets treated with a campden tab and brewing salts. Prior to starting the mash, I draw off some water for the sparge, which is not required, but I like to do it for the extra efficiency it yields. Pre-boil volume on a 6G batch and 90 minute boil is 8.12 gallons based on my system's variables. I no longer use Fermcap.