Can I switch the SIM card with AT&T?

I have an iPhone 4 and it has a cracked screen. I want to get the iPhone 5. I was wondering if i get the iPhone 5 will I be able to just take the SIM card out of the iPhone 4 and insert into the iPhone 5 and make calls, text, etc. With it?

You can buy a tool for a few bucks to get the SIM card out If you Look on the side of your phone, there will be a little dot with an oval around it that's where the SIM card is an you can switch it with the tool, I'm sure they can do it at an AT&T store as well