I am doing the same. I have a 5, and my mom has a 4. I will be taking her upgrade and giving her the 5. Since the the 5s has a nano SIM and your 5 is also a nano SIM, all you will need to do is switch them out once activated. I confirmed this by chatting with an Apple rep today through the "chat" method on their website.
I even asked if it would be ideal to just take the SIM out immediately upon opening, switch it to the 5, and activate the 5 as if it were new since you are technically just activating the SIM card/number. The rep said this is probably what they would do at the retail store.