5870 is long, ~11" from reviews on the net, some say 10.5" like anandtech, vrzone but i'm sure its 11".
I emailed Antec us n euro n us told me it "should" fit, euro told me "it won't fit if the card is 11", max supported is 10.5".
I think it will fit in Antec 300 without modding the case.