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earlier this year my mother’s iphone 5s randomly shut down despite it not being on low battery and couldn’t be turned back on unless you hold the power and home button, it happened twice today and i believe the battery is at fault judging from the symptoms but i want to make sure before a buy a repair kit.

You can’t make sure before buying replacement parts. Unless you have extensive technical skills in diagnosing board problems, all you can do is swapping parts to find out the bad one. The battery or the board or the system could be defective, start trying.