How to unlock disabled iPhone without losing all data?

Ok so I just got back from a Spanish trip which I loved and have 1000 photos of, if not more. My friend was looking at my messages so I quickly changed my passcode. However, I have already forgotten it. Is there any way that I can unlock the phone without losing all the data, contacts and photos etc?

Is it possible to back it up without unlocking it to my computer, then restore it and then restore from the backup?

Also, does anyone know the pattern for the timings of the phone being disabled? I have tried to guess the passcode at 1, 5, 15, 60 and now I think 24 hours, but what comes after?

I'm running iOS 7 on iPhone 5.

Yes you can simply backup your iPhone and restore it. Backing up your iPhone does not require you to unlock your phone nor does restoring it.