We're all assuming you want to play games, otherwise your integrated HD4200 is fine for productivity apps; maybe a HD5450 for movies and other video.
You don't list your monitor resolution, or the games you want to play, but unless the games are very demanding and/or your resolution is very high (more than 1920x1080), start with a single HD5770. That may be all you need. That's what I'm using at 1920x1080, but I know my games are not as demanding as many newer ones. If you need a second card, you can always add it.
Btw, assuming your mobo is this: http://www.newegg.com/Product/Product.aspx?Item=N82E16813157167&cm_re=Asrock_785-_-13-157-167-_-Product
, how do you like it?