A high quality 700 to 750 watt power supply with sufficient current (amps) on the +12 volt rail(s) can easily power a pc system with two video cards operating in Crossfire mode.
The recommendation for a pc system with three video cards operating in Crossfire mode is an 800 watt or greater power supply with sufficient current (amps) on the +12 volt rail(s) and six PCI-e video power cables of the appropriate type.
here is a link to an example of a high quality energy efficient power supply for your system:
For your setup corsair suggest 950w to 1000w for the 3x58XXs. With the 3x57XXs they suggest 750w to 950w. Here is the link to their power supply finder: http://www.corsair.com/psufinder/default.aspx
The 750w would be ok for a triple 5770 setup but would not suffice for the triple 5850 setup. Once you decide on the cards you will know your required power. I would go with a 850w for the 5770s and a 950w for the 5850s.