Verizon doesn't use SIM cards. You'll need a 3rd phone without a number on it. You take the extra phone and activate it with the number on the iPhone 4. Now that the iPhone 4 has no number on it, you activate it with the number on the iPhone 5. Then you activate the iPhone 5 with the number you had taken off the iPhone 4 and put on the extra phone. And your phones are then switched. Clear as mud?
Or Verizon can do it for you. But there are no SIM cards involved. You'll have to back your phone up in iTunes or iCloud and reset them then restore them after the switch.