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Is it posible to repair the home button, when it font work when pressed on, there seems to be no signal when dressing it down and the normal feeling of click is not there.
Yes you can. iPhone 5s Home Button Assembly Replacement Although it’s not so much repairing it but rather replacing it.
absolutely. you can buy a replacement part for it, and change it out. However, The touch ID will not function without pairing it to your motherboard. the software required for doing this is only obtainable for apple certification. The button will work, but you wont be able to use your fingerprint. you may be able to salvage the OEM part, by gluing a new nub onto the edge of the button, but i wont be able to guarentee that without actally having handled the button in a diagnosis.
It most likely needs replacement, but you might be lucky that it is just ‘stuck’ since you are not able to click it. If you are comfortable, open it up and try to take a look at it - Otherwise most repairshops would likely give a free estimate