5 minutes is way too fast to be getting to 220* from a cold start.
I'd suspect the gage or sender first.
Start the engine and run it with the rad cap off to see what's going on. Nothing should come into the top tank for 5-10 minutes, when the thermostat opens. (yes it may overflow a little) When it does open, you can take a direct measurement of the temperature. Be careful doing this...
