I doubt it. The 5770 is around 10% slower than the 4870. And if you compare the last gen, the 4770 was slightly better than the 4830. So the 5830 may even be slower than the 5770! But these are whole new cards so we'll have to wait and see but apparently ATI have got no more releases due this year so it will be a while.
Firstly, there's a big price gap between the HD5770 and HD5850. ATI can't leave the $200 price point wide open. they have $160 and then a $260 products, nothing in the middle. Now remember, that the price point we are talking about here is ATI's main sales price point, So they will not leave a gap like that, especially considering no one knows wtf Nvidia might do next (Nvidia seems like they just do what they want, and they might just be cooking up something to target that price point, no one knows, and this will scare ATI).
Secondly, performance! DUDE, do you realize that there is an epic performance gap between the HD5770 and HD5850, this isn't really ideal for ATI, as because of the difference between the two is quite large, but the so is the price. So either you spend less and get kark performance, or you spend lots are get nice performance. This isn't a nice decision to make. The gap is too big (price and performance), and it might actually mean people end up buying the HD5770 or an Nvidia part, which means that ATI makes less profit, and lose business to Nvidia.
So what to do? Well, seeing how some people have seen GPU's with 1120 stream processors, and possible 192 bit's, I think that might just be the HD5830, this would probably be between the HD4870 and HD4890 or @ the HD4890's performance level.