Hello, my question is: Does the gtx 580 runs fine in sli with my old gtx 470?
No, you will need another GTX 470 to pair up with your GTX 470. You cannot mix and match cards from different generations. The GPU's have to be the same for SLI. You will also need to make sure your motherboard supports SLI.
The only thing you can do to run both cards simultaneously is to have the 580 as the primary card, & keep the 470 for physicx