I think it is possible, but you will have to install both nvidia forceware as ati catalyst drivers. This is only possible on vista and 7 I think, so you can do that, BUT I really really don't recommend it.
First, improvements in real games are very minor with a dedicated physx card.
Second, the gtx 280 is way to good to spill it as a physx card.
Third, running two drivers at once from two different gpu manufacturers doesn't sound too good to me. I think it will result in longer startup times and even graphic problems.
Fourth, your 5970 is the most powerful card in the world at the moment. It should have juice enough for any game and if you do not agree, adding a card for physx will not result in a great performance boost. Go for crossfire in that case, which does not require another expensive 5970, but you can also use a 5850 or 5870.
Is it possible to have my 5970 as my main graphics card with an old GTX 280 as a physx processor?
I've always thought this couldn't be done but i really want to make sure as it seems like an appealing idea for my old hardware.
You can run the GTX 280 as physx along side the 5970 but you will need to use cracked drivers. NVidia has stopped allowing Physx to work alongside ATI cards without having modified drivers. As for physx itself, there are so few games that take advantage of physx that you would be bettter off just using the 5970 and selling the GTX 280.
@Griffolion, if you want to give this a try I can point you in the right direction, but as Deweycd stated the gains are only going to be used in a handful of games that use PhysX and a couple of BenchMark programs.