77 For a card like that, yes too much. There's a difference between normal temperatures and limits. I would think the cooler hasn't been seated well, I had a HD 7850 from Sapphire that only got around 65 degrees and that doesn't have as good a cooler as the Asus one.
If you're up to it, I would reseat the heatsink and add some nice thermal paste, if not, 77 is perfectly fine.