Can an iPhone 4s sim card work in an iPhone 5?

I want to buy an iPhone 5 but I dnt wanna sign a new contract is it possible to buy the phone and just put my iPhone 4s sim card in the iPhone 5? My dad would buy the phone cuz his contract is expiring then we would switch phones

No because the new Iphone is using a Nano sim or something like that. Its smaller than the one in the 4s.
I think you g#can get the one you have cut down.

No. The iPhone 5 uses a new form factor of SIM card called microSIM. You could sand it down to microSIM size if you're crazy, but no, it won't work.