Sorry, we don't get many women around here usually.
For 1680x1050 either will be very good. The HD4890 only really makes sense once you get up to 1920x1080. Even then it's a questionable value compared to the HD5770.
Basically the HD4890 is about 15-18% faster but it is older, hotter, much more power hungry, disproportionately more expensive and lacking in features. The HD5770 is $50 less, DX11 compatible, uses several times less power at idle and around half under load. It also supports 3 monitors like so;http://www.youtube.com/watch?v=5UeHJEeuLc8
if you are interested in such. Honestly I'd take the HD5770 over the HD4890 even if the price were the same, especially so when we are talking about below 1920x1080.