Actually I found is that with
moderate level of tessellation (not normal level), 1920x1080, 4xAA, 16xAF, besides the low frame rate dipping to around 24fps in the very beginning of Heaven Bench (due the heavy amount of tessellation I think), for the rest of the bench the overclock 5850 would pretty much remain at around 30fps and above.
Considering you are only on 1680x1050 res, I think it might be possible for you to get reasonable frame rate using
moderate tessellation, 4xAA, 16xAF. Your 5850 would probably struggle a bit at stock speed, but I think if you work at overclocking the card, it should give you good enough result on smooth enough frame rate.
Edited:
I ran the Heaven Bench at 1680x1050 dx11, 4xAA, 16xAF, moderate tessellation with my two stable overclock profiles (instead using the 1000core/1300memory). The settings are core900MHz/memory1200MHz/voltage1.240v and core975MHz/memory1100MHz/voltage1.265v, and here is the result:
From my previous bench, I found that by turn the tessellation from moderate to disable, it would give around 10fps high in frame rate (and that was at 1920 res, so for 1680 res it might give even more frame rate than that). So basically if you can overclock your 5850, you should be able to run the bench at 1680x1050 dx11, 4xAA, 16xAF, tessellation (disabled) with minimum frame rate at around 35fps.
But I have to say...with minimum frame rate at close to 25fps with moderate tessellation is not bad result at all.