Can I put my iPhone 4s sim card into the new iPhone 5?

My mom is switching to Verizon and wants to get an iPhone 4s more than the 5, she has offered to get a new plan with an iPhone 5 and switch sim cards with me and my iPhone 4s. Can this sim card swap happen? Will all my contacts switch to the iPhone 5? Or will the iPhone 5 reject the old sim card and visa versa? Knowing this will really help me make a decision.

Call Verizon.