If the A5X does go into the mini and Apple TV, it will have to be a die shrink anyways. This should mean cooler and more efficient, and hopefully also mean they can overclock it a slightly to keep performance above that of iPad Mini 1.
Overclock? The A5X and A6X run so hot Apple had to take the RAM out of the SoC package. The iPad mini has no such room for an extra extra RAM chip on the motherboard. It could probably could be jury rigged onto a AppleTV motherboard but then it would be useless for the iPad mini use. That could be ok if just soaking up Samsung wafer commitments they had already bought.
Apple would need to get rid of the heat problem to remerge the RAM back into the SoC package. If the shrink does it fine. If it doesn't then likely iPad mini will get an A6 derivative with a better CPU/GPU combo that runs more efficiently.