Why do you say the viewfinder does not go wider than 5.6? I thought until the time of the shutter, the aperture is fully open and so should be at the F level you are trying to use.
Maybe i am mistaken, but can you explain a bit more please.
That statement isn't really correct for the aperture - it's actually f/2.8. The focusing screens in modern dSLRs are laser microetched to make them brighter, so they work better with slow lenses which are common these days. One consequence of that is that the viewfinder shows the DoF of an f/2.8 lens even with lenses that are faster than that. If you have a fast prime, test it yourself - use the DoF preview button as you stop down from wide open, and you'll see that the VF doesn't start getting darker until you hit ~f/2.8 (or f/2.5 with some lenses). The high-precision Eg-S screen for the 5DII is a 'brighter' screen that shows the true DoF for fast lenses (but f/5.6 lenses are pretty dark, unlike with the stock screen).
I use an Eg-S on the 5DII, and the lack of a similar option for the 5DIII is very disappointing. It's true that there will likely be 3rd party screens as there are for the 7D, but the focusing screen on the 7D is not considered user-replaceable, and doing yourself is a challenge, so most of the vendors that sell 7D screens also offer a service to swap them out. Personally, I prefer the flexibility to easily change them out on-the-fly - Eg-S when I'm going to be using a fast prime, Eg-A (the stock screen) when using a slower zoom, like the 28-300L where I might be outdoors or inside.