I think 5 years is in order to let the biowarfare plagues die out. I am not a believer in "universal antidote" though I do understand the in game necessity for it. Any Project Member that came out of cryosleep would be dead within weeks when they encounter a carrier.
Actually, canned food is good to go. The alpha and beta particles will decay in a few days and gamma won't do anything to the contents. Just wash with warm soapy water.
I would think that the Project isn't counting on Libraries and Universities being intact within large and medium urban areas. Probably best to relocate survivors to very rural locations and give aid to community colleges and state colleges.
All those supplies can't be counted on. Sure it would be a major boon but, a few years with fire departments and most is probably lost to enormous fires that sweep through.