iPhone 5s is stuck on the Apple logo, displays a solid color, or isn't recognized in iTunes.
The phone display is stuck on the apple logo. How can I get out of this trouble mode and get my phone back to normal and functioning again?
Try to reset your device. This won't delete your data stored on this device.
- Press and hold the Sleep/Wake button
- Press and hold on the Home button
- Keep holding both buttons until the display turns off and back on with Apple logo on it.
Alternatively, you may go to Settings - General - Reset - Reset All Settings
If this does not help, restore your device to factory settings. Note that this will erase the data from your device.
Take a look this Apple Support article: Use iTunes to restore your iPhone, iPad, or iPod to factory settings - Apple Support.
As a final step, try the recovery mode. Turn your device off, then plug it to your computer with the home button pressed. Keep the Home button pressed until you see the iTunes logo on the screen of your device. After that on your computer you should see the iTunes window saying your device needs to be restored to factory settings. Click on the restore button.
https://support.apple.com/en-us/HT201263
If these steps don't work, contact Apple and ask for help.