I wish to factory reset my iPhone 5

Reset Restriction Password (Forget Restriction Passcode)

This solution requires the use of your computer.

First, you should understand that this method will not work with 'Find My iPhone' enabled, as that gives additional security, which in this situation is not helpful. You need to go to 'Settings' on your phone, and toggle 'Find My iPhone' off from under the 'iCloud' menu.

Please note that you cannot get around the problem of a lost Restrictions Passcode by using any variation of “Erase All Settings and Contents” on your phone. If you try to go this route, you will be asked to provide the Apple ID passcode and the Restrictions Passcode, the last being the very thing which you have lost or forgotten!

However you can reset restriction passcode by restoring with iTunes:

Step 1. Ensure that 'Find my iPhone' is off, and backup your iPhone.

Step 2. Connect your iPhone to your computer using a USB cable and launch iTunes. Be sure that your iTunes is updated to the latest version.

Step 3. Go to the 'Summary' tab, then click on 'Restore iPhone.'

Step 4. When asked to confirm, click on “Restore” again.

Step 5. In the 'Update Window' click 'Next', followed by 'Agree.'

Step 6. Wait while iTunes downloads the latest iOS and restores iPhone.

Now you'll be able to access your device without the restriction passcode.

Restore your iPhone, iPad, or iPod to factory settings - Apple Support