Your build looks pretty nice. Though are you sure newegg ships there?
If you can afford $50 more I would suggest getting a board which will support Crossfire. This way you can upgrade simply in the future, though maybe you have no intention to? If getting a Crossfire board make sure its x8/x8.
Also if you don't get a crossfire board and don't plan on Crossfiring or upgrading I would suggest getting a smaller PSU. 500 or 450W will be plenty.
I would prefer a Cooler Master Hyper 212 Plus over that one. It has a 120mm fan and is very nice.
Total should be under $750 for sure. That Asrock 870 motherboard supports crossfire 8x, 8x mode so you can add another hd 5770 down the road, but for now one card should be good for your resolution. As Wolygon suggested, the hyper 212+ is would be the better option for cooling your cpu. Also cl7 1600 ram is the better option, but it's not that big a deal.
Strictly from a $$/frames P.O.V i would settle for say a 770/785g chipset, put SATA/USB 3.0 on ice all in the name of nabbing say a GTX 460 in there? Also WD 640 Black is a tad over priced so if u could do with 500GB have a looksy at Samsung F3 or Seagate 7200.12 500gb?
If 19th October isn't a bridge too far the HD 6000 series would be unleashed upon us hehe