In all likeliness, I guess you should expect somewhere around 40+ FPS on medium or high presets on that resolution. Without AA and AF. Though I maybe understating what a 5770 capable of. That's the best bet I could give you. That's enough to warrant playability.
And your system is quite balanced, I must say.
To get 60+ Ultra, I guess you'll need an additional core and a much more substantial GPU.
battlefield 3 is very much so a gpu intensive game. it can make due with really old shitty processors.
here is about the best example of this. http://www.techspot.com/review/458-battlefield-3-perfor...
it clearly shows that you have to get all the way down to a a6-3650 to see any fps hit on a gtx 580. so your totally in the clear with a 5770.
i just replaced my 5770 with a 7970 but i played the beta with my 5770 on 3 27" monitors with high settings and it was playable. and since processor doesn't matter until its crappier than yours, your quite safe. especially with such a low res.