some will depend on where/when you're going to hunt- archery vs late season, low desert vs above treeline; also going to be dependent on your gear- if you own a bunch of UL gear you can get by with less volume
having said that, for 5-7 days, I would be looking at ~ 6000+ cubic inches- 7 days of food takes up a lot of real estate
I’d say a 7800 because that’s what my fulcrum is and I can’t really imagine ever really wanting or needing a different pack at this point. It’s perfect. I guess with 2 medium pockets it’s more like 8400.
I’ve used a 3500 bag for ten day trips twice. I also had a hunting partner that split gear and chow. I try to go with the smallest pack I can get away with because I have a tendency to overpack.
A good rule of thumb is about 1000cu. in./day. So as mtwarden stated; ~6000 or so would be ideal. This isn't always true obviously, and depends on your gear/how well it packs, but food does take up a lot of space at the beginning of any trip
Pack design makes a difference also. I have a Stone Glacier 5100 and lid which I think is 500 c/i. I can easily fit gear for 10 days with the pack. Food goes in a bag on meat shelf and everything else goes in the bag with some room to spare. Also depends if you want to hang a bunch of stuff off the outside of the pack or prefer that everything goes inside.
I have never done the backpack hunt but a lot of these guys are very experienced backpack hunters. They have their gear lists figured out. As a new backpack hunter you will probably be packing more than some of these guys.
I use a bounty 4500 and it works good. I have done a 6 day turkey hunt with it. However I left some food at the truck because it didn’t fit. I just ran out of space. That being said I set it up that I came out to restock on Sunday. Sunday is a no hunt day in both Pa and Nc so it seems to work well for me. If I were hunting that duration in a state that had no hunt days I would need to upsize my pack so I didn’t waste a day walking out to restock.