Beetle
Ok, normally rooms have separate circuits or separate breakers. So if your rooms are on separate circuits you should be fine. You first need to determine this by shutting off breakers and finding out what goes where in each room to determine if each affected rooms outlets are on separate breakers. You need to find out how many amps these new AC units draw, it should say in the manual. Obviously if you have 3 units that each draw 10 amps each for example, a 15 or 20 amp circuit wont handle them because that equals 30 amps and it will trip. If the circuits are separate then you dont have to total them up. On the very tip of each breaker there should be a number molded in the plastic, this is how many amps that circuit can handle maximum before it trips. Never replace a breaker with a bigger breaker. This can cause fire. Call an electrician and have him double check everything to be safe.

Thor
Air conditioners might draw 10 to 15 amps for a second (literally) to start but immediately the draw falls to like 150 watts. It is not a big draw. The only problem is if more than one is on the same circuit and they both try to start at the same time. That can trip a breaker. 5200 btu units are not a big draw running.