Broken iPhone 5s screen, can't authorize iTunes
Ask Apple if there is a store near by. Usually they charge $129 (plus tax) to fix a broken iPhone 5s screen. If you can't get to an Apple store, you can mail your device in to Apple for a shipping fee of $6.95. If you purchased AppleCare+ ($99 for two years) for your device, you'll only have to pay $79 for a screen repair -- though AppleCare+ only covers two incidents of accidental damage. If you don't have Applecare+ you can choose a reliable supplier to buy a screen replacement and then do the repair by yourself or a repair man.