Yeah, your MLT size is going to be a critical factor. If you can hold 10-15 lbs of grain you should be fine for most average beers, but not the high gravity ones.
Also just so you are aware, you are probably going to get pretty poor efficiency as a whole unless you do a partigyle or similar where you can save your second/third runnings for another batch.
I tried making up a quick recipe for a 1.052 APA in Beersmith using a 3 gallon pot and 5 gallon cooler just to see how it would pan out, and the pre-boil gravity was 1.109.
So, there are a couple of issues:
1. Unless you are collecting second and third runnings for a second batch, you are basically throwing away money on grain just to get a 5-gallon recipe to fit into the BK.
2. Because your boil gravity is so high, this also drives up the amount of hops you have to use to get the same level of bitterness. So, you are also spending more money on hops.
If it were me, I would look at the long-term costs of trying to do a partial boil, and instead either do a split batch in two pots, or get a bigger pot. Partial boiling isn't a very good solution in my opinion, even though it is technically possible. I suppose the other option would be to stick to 2 gallon batches.