Yup, do this. You need to do it on both the phone and the head unit. The issue is partly that your iPhone 5 "remembers" the pairing, but the head unit doesn't recognize your iPhone 5 (different device). You have to re-pair from scratch.agreed.
delete the phone from the headunit and repair using the bluetooth audio option... or, whatever it's called.
report back and we can try to help further.
joel