If your 5S has a sim card in it, it should have already been activated under your account. If you have LTE data working, you should be good to go. I would just advise against leaving your old sim card in your iphone 5 if you sell that phone.
I would suggest to do the trade in on the iPhone 5, and the sim card should be good to go for when you turn on the device, if you have any other questions they should be able to help you in Customer Care, 1-800-922-0204 if you have any trouble or just want to have someone there during the activation if you have any questions. Just make sure you have everything backed up to the iCloud before you do the swap and my suggestion would be to not remove the sim card from the 5s and to take our the sim card from the current 5 and put it in a box of old cellphone junk just incase.