What other cards should I consider? I like to stay with AMD.
The next performance level should be the "old" HD7750 one, which nowadays I think it's rebadged as the R7 250E: to be fair, even the plain vanilla R7 250 should offer a small performance bump over the 5670, but it should be barely noticeable.
On the other hand, while you can find several passive R7 250 in the wild, currently I'm not aware of any silent-out-of-the-box R7 250E (or 250X, equivalent to the 7770), so I can't help with any specific advice.
Among past generation cards, set aside some rare passive HD7750 cards, at least a couple of XFX HD7770 ones may run virtually silent, if you can find them (very unlikely now): there were the FX-777A-ZDF4 and FX-777A-ZDB4 (you have to tweak the stock fan profile using either Rivatuner-derivatives or SpeedFan to lower the fans speed under 700rpm).
What about your budget?