It seems to me that the 5D3 LCD shows colors slightly more accurately than the 7D and vastly more accurately than the 5D2. It seems to have about the same general accuracy as a stock new iPad using a stock image viewer. Doesn't quite match a well calibrated monitor though, colors are slight bit different and WB a little moreso. The 5D3 and 7D are close enough to at least be able to get a general in field sense of what WB matches the real life scene though. The 5D2, not so much.
For in cam jpgs/movies on the 5D3 it seems that profile Faithful gives the truest colors overall for stuff shot under direct sunlight or bright indirect sunlight, very late in the day or in deep shade or with odd lighting then it seems Neutral is better overall. Landscapes gives the most bizarre colors, by far, of all the profiles and Portrait the next. All the profiles oversaturate things, Standard and Landscape and Portrait a ton, Faithful a fair amount and Neutral a touch. Contrast -1 to -4 and saturation -1 to -3 is often a bit truer to life, that said, since no camera captures what the real experience is like, sometimes a modest artificially boost can be more natural in the end, it depends.
In ACR, Adobe Standard seems to give the most natural overall colors of all the built-in 5D3 profiles (you may need to knock down saturation a tiny bit though), although I found that under stadium lighting they all went wacky other than Camera Standard.