iPhone 5 to iPhone 5s SIM not Compatible

I purchased an iPhone 5s this morning (Verizon 64GB, Black), I already have an active iPhone 5 on Verizon. My plan was to swap the SIM from the old to the new and I ran into a ton of problems.

iPhone reported "SIM NOT VALID"

iTunes Reported : "The SIM Card inserted in this iPhone does not appear to be supported"

I guess I was over thinking it, just hung up the phone with Verizon. Here is all I need to do to upgrade:

1) Leave old SIM in iPhone 5

2) Leave new SIM in iPhone 5s

3) Power down old iPhone

4) Power up new iPhone and connect to iTunes and let it activate and restore from backup.

So, don't overthink it if you are upgrading as the new iPhone needs the new SIM.