Q: iPhone 5 not recognised on iTunes - nothing works

Give these suggestions a try.

If you don't see your connected device in iTunes for Mac - Apple Support

Get help with iOS update and restore errors - Apple Support

Check your USB connections

Errors: 13, 14, 1600, 1601, 1602, 1603, 1604, 1611, 1643-1650, 2000, 2001, 2002, 2005, 2006, 2009, 4005, 4013, 4014. You might also see a message that includes "invalid response."

If the USB connection between your device and computer is interrupted, you might not be able to update or restore.

To narrow down the issue, try different equipment:

• Use the USB cable that came with your device, or a different Apple USB cable.
• Plug your cable into a different USB port directly on your computer. Don't plug it into your keyboard.
• Try a different computer.
• Solve other issues with the USB connection, then with your security software.

If you still see the error message, check for hardware issues.

I know you have already tried most of the recommended procedures to no avail. Try this one as perhaps another shot, a different way to approach the issue. Make sure you follow the steps precisely. I hope it works but if it does not, your best bet at this point might be to contact an Apple Store.

Connect the charging cable to a USB port on your PC.

Open iTunes.

Turn off your device if on.

Press and hold the power button on your device and don’t let go.

Connect the cable to the iPhone while keeping the power button pressed down.

Wait until the PC detects the device and wait for it to restore.

Good luck,

elcpu

It's a hardware problem. Make an appointment and take it in to have it serviced / replaced.