It should be ok. there are better PSU's out there, but this one will definitely work. The specs on the website say its high efficiency, and has 60amps on the +12v rails.
This is much higher quality than Thermaltake's lower wattage power supplies.
My suggestion is to try it, and if you think the PC is getting too hot or the psu fan is running too hard/etc you can swap it out for a bigger one.
The new technology in the 5870 card means it has lower power requirements than you might expect from a card in this price range.
If you had to buy another (which you wont have to) the best PSU manufacturers in reputation are probably Seasonic, Corsair, Antec and OCZ. (I am biased toward corsair because i have one)
Among these brands you would want to pick one thats very high efficiency and has a high amperage on the +12v rail(s). Picking a higher wattage unit than you need will make it run slightly more efficiently.
Thermaltake has a bad reputation because they make some very cheap and low efficiency models, but they make some good models too-- like the one you have.