If you really want speed and DX11, you really need to avoid those cards. The 57xx series are very good for the price and performance is great, especially with the 5770.
The 58xx series are much faster and much better but at a higher price than the 57xx series.
The 54xx and 55xx are budget cards and will not give you very good performance. Yeah, you'll get DX11, but at what cost to the performance?
If you're not looking to game, but do video capturing, editing, watching, then yes, the 54xx or 55xx series are good for a HTPC.
Since you are wanting DX11, I'm assuming you want to game. Therefore, avoid the 54xx and 55xx series and go for the 57xx or 58xx series instead.