With a 5770 you'll be able to play those games with the settings mostly on high, but the HD5770 is a mid-range card. It has a good price and delivers a good amount of performance, but it's not something for extreme gamers who wants to max out every single game.
Coming down to a wrap up, it's a good card, and will handle several games on high, but not all. But if your budget isn't very healthy then I would recommend the HD5770.
If your mobo has 2 PCI-E inputs then you could get another 5770 later on if you'd like to and run them both with crossfire(Two cards).