>>1803708>good shot placementPerhaps if you hit the eye. 5.56 (which I assume you meant, as I'm not aware of any .556 caliber) is literally designed not to kill. One of the reasons the NATO changed from 7.62 to 5.56 was so that enemies would only be wounded more often, making casualities place more strain on enemy supply lines. And if a caliber won't even kill a human on a clean, center-mass hit, you can't expect it to kill a bear.
If you expect to need to defend yourself against a charging bear, nothing beats a solid hunting spear. Once you manage to impale the bear through the lungs, he can't reach you due to the spear's crosspiece stopping him, and will die within seconds. Next best would be a large caliber, fast-shooting handgun - it might not stop the bear immediately, but you still have good chances of it dying before it kills you.
If all you have is an AR15, your best bet is to wrap some bacon around it, throw it at the bear and hope he feels like playing fetch.
