I have an iPhone 4, and want to upgrade to an iPhone 5. Can I just buy one and switch my sim card?

I have an iPhone 4, and want to upgrade to an iPhone 5. Can I just buy one and switch my sim card?

Yup pop the one out in the iPhone 4 and put it in the 5

No, You will need to get a new sim and your number transferred over to the new sim.