I was hoping for some +12V specs for the PSU. But that's OK. I pretty much know you will be limited to a very narrow card and one that is LOW powered. We still don't know the length available for a card, since you didn't measure. But yes, that HD 5570 would be a candidate along with these:
http://www.newegg.com/Product/Product.aspx?Item=N82E16814150677
http://www.newegg.com/Product/Product.aspx?Item=N82E16814500352
The R7-240 and HD 5570 are about equal performers, the 240 being newer. The GT 720 would be a bit slower. But you are not going to be able to make a gaming machine out of that slim line PC. Maybe a 720p gamer at best.
Keep in mind, we don't know for sure if any of these will fit until we know how much length you have available in the case.