Echo that. A month without email would suck

Honestly, after a week, I think it is unrealistic to be packing more food. You'll have to procure it- five days of chow, and fishing and snaring gear. Maybe a .22 or high end pellet pistol or slingshot, but those are iffy if I'd include them.

Hygine. You MUST have a tooth brush at the very least. Have a set of clothes sealed up for the packing out if this is a voluntary thing. That way, you don't scare people when you get out.

Saw or axe would be critical.

But if you've got a solid wilderness kit, you should be good if you've planned things out and have the skills.