Error 53 in iTunes is Touch ID related. It can appear to an iPhone 5S, iPhone 6 and iPhone 6 Plus, if the unique Touch ID sensor cannot communicate with the CPU. If you are having a hardware issue with your iPhone (broken screen, muted sound etc) and you are trying to fix it yourself, it is strictly recommended that you make a backup before attempting any internal changes. During screen replacement you can easily damage the ribbon cable connecting the TouchID sensor with the mainboard, leading to a state where your device is bricked and you simply cannot restore it or update it. Neither jailbreaking tools nor any other method can bypass the specific problem, no matter how many times you try. Do not try to replace a screen if you are not an experienced technician in these models, as long as you don't want to end with a bricked device. I had the same issue with an iPhone 6 16GB and replacing the little ribbon cable solved the issue instantly (ebay cost 3$). I think that I've helped you! Good luck with your repairs ;-)