Jailbroken iPhone 5s stuck in boot loop and can't be seen by iTunes
You can enter DFU mode during a bootloop:


Connect the device to the computer and open iTunes. It won't be detected—that's fine.
Hold down the power and home buttons together.
The display will turn off, then an Apple logo is shown. Keep holding until the display turns off for a second time.
As soon as the display turns off the second time, keep holding home but release the power button.
The display will remain blank and iTunes will prompt you to restore the device. Now release the home button.