I think the 5870 is overkill the 5850 will do nice... I think PSU wise will have no problem with 5850/70... I do not want to answer the others because I don't really have the experience... You also have to double check whether the case you selected can fit the graphic card... And Whats up with dual core, get an AMD Triple X3 720 or Quad X4 955 or i5.... otherwise the 5850 MAY bottleneck your CPU.... I'm not too sure but just assuming.
The 5770 doesn't perform as good as the 4870 and is similar in price with 4890 after rebates. If you're not going to be playing any game using DX11 any time soon (as in the next year or so), it might be cheaper to get the 4800 series graphic cards for now. You can always upgrade to DX11 when it becomes main stream or whenever you decided to get a new system.
For the CPU I think x3 720 is a good buy if you're overclocking, and having three cores is plenty for most of the applications on the market at the moment.
I5 is a case of buyer's remorse waiting to happen. If you don't need the performance, you'll regret not spending more of your budget on a stronger GPU [and getting a lesser but still adequate CPU like an AMD 720BE]. If you DO need the performance, you'll regret not waiting until you could afford the i7 with hyperthreading, higher turbo-boost, and possibly triple-channel RAM (on LGA1366).