The pictures in the eBay listings are of the Apple HD5770. I have a couple and can confirm, hence fake. If the seller had genuine Apple HD5870s for sale, he wouldn't have had to scour the net for generic pictures of the wrong card. Caveat emptor.
Also, the price is ridiculous. This is a listing on the UK site:
Some can be had for even half that. The price has tumbled as the Mac Pro cheesegraters have aged and fallen far behind in performance compared with even recent Mac Minis. There isn't the demand for these that there were, especially as the 2010-2012 Mac Pros can use non-Apple graphics cards and still provide bootscreens. Additionally, the HD5870 is a non-Metal card so no use on anything past High Sierra.