Eyefinity will only work with the display port. Just get an active DP to DVI adapter, such as these: http://www.newegg.com/Product/Product.aspx?Item=N82E16814999032
http://www.newegg.com/Product/Product.aspx?Item=N82E16814999030
Without an active DP adapter, you can only do clone or extended desktops.
By the way, the 5770 handles multiple displays at 1080p very well.