I'm thinking about buying an HD 5870 and I'm not exactly sure how it will perform on my 1080p 40" LCD. Do all 1080p HDTVs have the same resolution of 1920x1080 no matter the size of the Tv? Can i compare the performance of this card with high res monitors to see how will it will perfrom on my HDTV?
Yes, all 1080p display surfaces have the same resolution, and therefore the same number of pixels, and therefor the same load on the graphics card. When looking at benchmarks, the load of a 1080p screen will be somewhere between that of a 1680X1050 and that of a 1920X1200. I think that a HD 5850 should be more than powerful enough for you.
Any "True HD" television should be 1080p. And all 1080p is 1920x1080 resolution (minimum). The size of the TV really won't affect performance at all. Whether it's a 32" 1080p, 40" 1080p, or 56" 1080p doesn't matter. It's still the same resolution.