Chosen Solution

Is the touch id button the same on the 4th and 5th gen ipad air? How to fix it and save the touch id function?

I haven’t worked on either the fourth or fifth gen iPads, but based on my research this button is the same. As for repairing it—there is no way to keep Touch ID if you replace this button. The button is paired by Apple to its original iPad and they have not made the software to do this available. Even Apple stores do not repair iPads (they only replace). Replacement buttons are available so you are at least able to get a functional power button. Finding a guide that makes it clear how to do the repair is a bit trickier. But you can have a look at the teardown to get some idea of the internal layout.