Ax -- An ax is just a gimme. Anything you need to do with a knife you can do with a sharp ax, and axes are much better for buildings shelters and fires. The colder the weather, the more you want one.
Thick sided metal water bottle -- You can boil water in it, and then carry it once it's safe to drink. I'm tempted to say a metal cup, but the container wins. If it's not cheating, a metal canteen with a canteen cup fitted to it would be the best of both worlds.
Full Bic lighter -- There are fancier options and longer lasting options, but there aren't many more convenient options. They're also small and inexpensive. I use these when I feel like starting a fire and not playing around.
Rain-proof shelter -- A big tarp, a poncho, a tent. Whatever. The tarp is probably the most flexible in terms of what you can do with it, since you can build a variety of frames to put it over/ under/ around. If I went with a tarp, I'd want cord tied to the grommets.
A week of food that stays well without refrigeration -- I know you can live for a week without food, but I'd rather not. I get grumpy after about a day without eating anything. I can't imagine how crappy I'd feel after a week of scrounging for berries and bark and hoping that a dead fall trap worked. While I could pretend to be bad-ass and go for peanut butter and say that I'm going to trap a bunch of animals, I'd much rather just sit down, enjoy nature, and eat something out of a package.
That's enough to stay dry, relatively warm, hydrated, and fed. Time could then be spent improving shelter, building wind breaks, and doing similar things.
I guess if I was cheating:
1. A cabin with a fully stocked kitchen
2, 3, 4. Lovely women
5. A well stocked liquor cabinet