I recently purchased a Dell Optiplex 380 and just need a fairly basic card to run some games on medium-ish settings. I don't have my exact specs at the moment, but my monitor display is 1600x900 and I believe it said it had a slot for LP PCIe 2.0 and x16. I'll update with more specs later if necessary.
Assuming you meant the E5800, the closest I get at http://www.extreme.outervision.com/PSUEngine it looks like your PC with a HD5670 added would need 214W; that's without any capacitor aging. If you got the 80+ version of the PSU, it's probably good for that, but I wouldn't trust the standard one, at least not for long.
A GT430 shaves 5 watts off that, and a HD5570 uses 10W less. Either of those would be marginally safer.
Edit: As much as I hate this expression, "OMG!" I just priced this thing on Dell's site. If you paid $700+ for this, you got rooked.
Went with the HD5570. I was a little concerned with the size of the 5670 (along with my PSU) and didn't think the performance difference would matter too much for my purposes (although the 5670 actually had a larger rebate yesterday and cost $3 less). I'll update later how it works out, thanks again everyone for the advice.