Aircraft are not designed to be as reliable as possible by throwing in unlimited amount of redundancy. Usually if an environmental factor affects a sensor, it has a very high chance of affecting other similar redundant items (Remember the birdstrike and landing on the Hudson?).
In fact this is a frequent item of discussion when one is deciding between a single engine airplane and a twin. A twin engine has double the chance of AN engine failing and dramatically less chance of both failing at the same time. Unless an environmental factor was the cause of engine failure. And too many deaths came from just one engine failing and pilot trying to fight the remaining engine instead of focusing on a forced landing.
Most aircraft systems (check out the technical differences between non-TSO and TSO GPS, steamgauges etc) are designed to INDICATE a failure and stop working when there is a failure, rather than try to be as reliable as possible. This way, the pilot has an option to switch to a completely different system. Of course you need some redundancy, especially if the other item works in a different way.
So 5 AoA indicators would not be as good a design as a single AoA indicator that can reliably flag a failure. Since it can't two indicators can show a failure by showing the disagreement between them. Just fly through icing if you have 5 indicators and you'll see why that's not as good an idea. Once a failure is flagged, a pilot can disable systems that depend on it (if not done automatically) and remain in control.
Ideally a transducer that does not depend on vanes (maybe some kind of movement/capacitance sensor that can sense the movement of air along its surface) would be a perfect backup.