The 5D does get more photons, but over a larger area. The number of photons per square mm is exactly the same on both cameras.
Noise is added to the image signal from the sensor, 60% of noise is caused by heat within the sensor, the more heat the more noise, it's electrical noise. Larger sensors need more energy to heat them up than smaller sensors do, therefore larger sensors have less noise. Used to be true, but not necessarily so these days, if you reduce the current the sensor requires it will run cooler and you'll get less noise. There are more efficient sensors than those made by Canon which are relatively old technology, the sensor in the GH2 is one of these more recent ones.
Most of the other 40% of noise comes from the A/D converter, or more especially the high impedance connection from the sensor to the A/D converters, by simply integrating the A/D converters within the sensor the noise from this source is virtually eliminated. The GH2 sensor has this feature too.
This noise threshold is ever present in all digital sensors, lower on modern sensors than older ones, the only 100% way to get zero noise is to use more light, then the exposure is well above the noise which is why movie companies spend loads on lighting the scene, if you want it to look dark, record with bright lighting and then turn the exposure down in post processing, result, dark moody image without noise.
Chris