A follow-up. Is a
So you don't think my 5-gal cooler would be big enough?
Back to the OP's question...
I've been using a 5 gallon round cooler with a BIAB bag for several years.
Yes you can do 5 gallon batches wit it if you do a batch or fly sparge.
Use the "can I mash it" calculator found here:
https://www.rackers.org/calcs.shtml
If you are stovetop brewing I wouldn't get a 10 gallon kettle.
A 5 or 6 gallon kettle will be fine for 3 galllon batches.
I also use a smaller, 16 quart pot ( I have a few I found at goodwill cheap) during my brew day when brewing smaller batches. I can heat up my mash water faster on the stove using two smaller pots than my big brew kettle, also, its easier to dump the hot water into the mash tun with the smaller pot.
I then heat up the sparge water in the small pots and drain the first runnings directly to the kettle from the cooler/mash tun.
I have some bigger equipment for outdoor brewing, but the smaller kettle is easier to handle and clean.
I like using the 5 gallon better bottle fermenters instead of using a bucket.
If I'm brewing a high gravity beer that is going to be aged, I'll brew a 3.5 gallon batch and ferment in a 5 gallon carboy, then transfer to a 3 gallon carboy for aging, filling it all the way up.