If it's not the same chip as the iPad 3, why could it be called A5x?
All the battery boost it's going to receive is going to be sucked up by the LTE and the new screen, and a power-hungry SOAC is going to be the last thing they put in the new iPhone.
It's going to keep the same frame rate as the iPhone 4S on the new resolution, and it's going to be more powerful than the A5, we agree on this. But it's not going to be the A5x, which is overkill for both graphics power and battery life. It's going to be a 32nm dual-core, simple as that.
Apple is not going to play the quad-core war because it doesn't make any sense on smartphones. The best chip you can get right now on Android is the Qualcomm S4, which is a pure dual-core. There is nothing wrong with the iPhone 4s performance, and the iPhone 5 is expected to mantain the same kind of performance with a slightly improved resolution (I expect 640p at 16/9). For these situations, a die shrink is far more adequate, because it reduces the needed power (which will be needed by the screen and LTE) and mantains the already optimal performance of the iPhone 4s, slightly boosted to cover the higher resolution.