it would fit since the mounting is exactly the same. it hasn't changed since the HD2k series. but would it be worth doing? no. better off buying an aftermarket heatsink then to attempt to use a heatsink designed for a much cooler running gpu. not only that but you would already have to buy ram/vrm heatsinks to cool the rest of the card.
It might work, but I would not recommend it. The 5850 and 5770 have different thermal thresholds, with the 5770 being the far lesser of the two. In short the 5770 cooler might be adequate to cool the 5770 card, but not the 5850.