How to remove Iphone passcode? - 1

Recently I broke my Iphone 5C and got another phone. I logged into the icloud and all the recent stuff that I had saved onto my broken Iphone 5c in't in the icloud because I didn't have enough storage to do a backup. Well I tried to do a backup on itunes but it won't because my iphone needs to be unlocked but the screen is broken so I can't get into it. I've tried to look up how I can remove the passcode but most will result in losing all the stuff I have in the phone already. How do I remove the passcode without losing any stuff?

Buy an iphone hdmi lead that you can plug into the back of your TV and you should be able to see the screen coming through the TV, that's how i watch Netflix xD