Ouch, no way. Not even in the realm of required.
Firstly, and I'm only mentioning this for folks who don't pay attention to the numbers of the cards you're going to use (different on paper, but identical in chip tech, as I'm sure you know) putting two generations into CrossFire will make your faster card throttle itself down to the speeds of the slower card (both in terms of clock speed and feature set), so you're actually doing yourself a disservice by mismatching the cards like that. Since the 6770 = 5770, it's a moot point for you, but I wanted to be sure folks saw that info in case they find this thread later and create more issues with a non similar family GPU setup. :\
Secondly, for those cards, 850 watt is overkill if you get a name brand power supply. You can easily run that setup on your existing PSU, or if you're feeling skittish about it, 600-650 watts should be fine. Two 5770's in CF only use up about 384 watts, and you'll see nearly identical performance with a 5770/6770 setup.