I just got me a New Anderson gun and I was wondering can I shot 223 and 5.65 out of it

Is it 223 Wild Barrle

Like Kyle said man. If the barrel is marked 5.56 NATO or .223 Wylde then its good for 5.56 or .223. But a regular .223 chamber cant take the pressure from the 5.56 round.

If your barrel says 5.56 or .223 wylde, yes. If it says .223 remington, no. Your barrel most likely says .223 wylde so yes you can.