When you need to factory reset your iPod Touch 5th generation without a password or iTunes, it can be challenging but not impossible. Here's a step-by-step guide to help you achieve this:

1. Turn off your iPod Touch by holding down the Power button until the slider appears, then slide to power off.
2. Press and hold the Home button while connecting your iPod to a computer. Keep holding the Home button until you see the iTunes logo and a cable on the screen.
3. On your computer, open iTunes and look for a message saying your connected device is in recovery mode. Click 'Restore'.
4. Follow the on-screen instructions to reset your iPod Touch to its factory settings. This process will erase all data on the device, including the password.

Remember, this method will remove all data from your iPod Touch, so make sure to back up any important information beforehand. If you encounter any issues, seek professional help to avoid causing further damage to your device.