DX 11 effects has a performance penalty especially Tessellation. Basically you are asking you graphics card to do more visual effects. The more you demand of it the lower the performance will be. Like going from 1680x1050 to 1920x1080 resolution with that card.
The HD 5570 is a fairly weak card. It's more of a multimedia card than a gaming card. The HD 5670 was considered to be an entry level gaming card.
If you are going to upgrade to Win 7 solely for DX11, then also save up money for a new more powerful video card.