Each card occupies both 6pin on the motherboard. Can the 5870 run with no AUX power? Can each 6pin on the motherboard be split into two, so both cards share the same 6pin (power)?
You need pixlas mod or separate PS to run both of those. They need equivalent of 8-pin each. (2 6-pin = 1 8-pin).
Can the 5870 run with no AUX power? NO
Can each 6pin on the motherboard be split into two, so both cards share the same 6pin (power)? Not for these two cards
A follow-up question: Will OSX (or applications) be able to take advantage of a pair of non-identical video cards?
Okay. Like the regular Davinci or those bitcoin mining software. I guess it won't benefit my regular usage much. Thanks!
No, only very little software can use multi GPU properly. And almost none of the normal daily regular usage can utilise that. If you has a RX580, then all you need should be just the RX580, the 5870 should be quite redundant in normal daily use.