Sapphire's own website is useless and doesn't specify card dimensions.
I would suggest you go to a store and take a tape measure with you,
Cuz i just googled Sapphire 5770 vapor x and got results on dimensions varying from 8.5"- 10.5".
Like ct1615 says i can't see the majority of 5770's being longer then 9.5".
I just checked the XFX site and every 5770 they make which is quite a few are all 8.5" long.
So add another 3/4" for power connects.