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+/- 5% is the acceptable range. For the 12 volt line, you can accept as low as 11.4 volts or as high as 12.6 volts. For the 5 volt line, you can actually allow as low as 4.75 volts.
Now, my question is where you're getting those measurements from. Motherboard sensors can't be trusted to give reliable voltage measurements. You should use a multimeter or similar device to get an accurate reading. If you're using a multimeter to get those readings, let's discuss requirements for your new power supply...
As I read in another post, someone mentioned that the voltage sensors are actually NOT all that wrong. It is the true value with the resistance on top so somehow if you add the resistance you will get your true total voltage values.
Still, you can't know how far off the measurement is without using an absolute measurement via multimeter or something. Thus, it defeats the idea of using the motherboard sensors simply out of convenience. Do motherboard readings make a good relative indication of voltage levels? Sure.