Need to reset to factory settings without entering password as iPhone keyboard not working properly.

I have a problem with my iPhone 5 in as much as the keyboard and screen has stopped responding to touch. Not all areas of the screen, just enough to make my life difficult and for it not to be able to recognize certain numbers and letters that are contained in my password. (It's also making it extremely difficult to respond to messages and phone people).

So, I've tried just a normal reset and that didn't work. Turned the phone on and off etc. The next stage is to reset to factory settings via iTunes but its asking for me to enter my password on the phone. I know the password, I would love to be able to enter it but the keyboard just isn't working.

I'm not sure how to get around this? Does anyone have any ideas apart from getting a new phone?