I'm gonna make a PC for beginner's video editing with software not with a EDITING CARD like MATROX's.
By now there is not enough money to pay for a NVIDIA quadro also.
My question is if I use a P55 mobo with a CORE i7-870 Processor for rendering, is it matters what graphic cards
I have to use?
Then, is there any differences between a AMD 5870 and 5770? what is your suggestion?
Go big on ram (as fast/ best timings as possible) and CPU cores.
 You might want to think about the AM3 platform because you could get more cores for your cash.
Slim on the video card to save money (you don't need the fastest video card for video despite idiots that think they know what they're talking about might tell you. All you need is one that has the most hardware decoding which i think is the gf104 series or something (someone will chime in and correct me if im wrong) like the 450 or 240.
To answer your question, if you plan to have fun, then fin, grab a 5870, but if not you can put the cash saved from going with a 850/770/830 and put it to the ram...
Any specifics? If your main concern is rendering, you may want to get an i7-9xx series or a much cheaper and stronger Phenom II X6. This is mainly all you need if the bulk of what you do is rendering with things like x264 and aviSynth. However, if you're using stuff like Premiere or After Effects, throwing in a bunch of ram is going to help. If you're going to use CS5 a good nVidia card can actually give you some previewing benefit, as CS5's live preview engine is CUDA accelerated. Alternatively, if you do FFT noise reduction with AVISynth, you can also get a CUDA accelerated version of that plugin and an nVidia GPU could help out there too.
Without at least a bit more info of what you actually want to do "Video Editing" is pretty vague, and can range from anything like, get a really highly core'd CPU to needing a really strong CPU, lots of RAM, and a decent CUDA GPU.