what is your screen resolution? here's tom's review on the 7770 when it was first released: http://www.tomshardware.com/reviews/radeon-hd-7770-7750...
at 1980x1080p, it was getting 46 frames per second on average. which is pretty playable. drive updates has also improved the 7*** series cards by a lot, so yeah, I'd say you should be able to enjoy the game on high settings
I'm not feeling it. The techpowerup review shows 34 fps, which is right at the minimum and isn't being played with the Hi-def texture pack. Skyrim has wild variations in fps depending on the location. You need to be hitting 40+ fps in a review like that to make sure you have all the diverse settings covered with sufficient performance. I would be concerned about that card in Skyrim.
Thank you! And yes my screen resolution will be 1920 x 1080p. I say will be because I am getting a new computer and plan on playing many new games such as Skyrim. I have it for PS3, but the PS3 version is incredibly laggy.