iPhone 5C broke, need to back it up.

I was playing with my iPhone 5C when I pressed the screen too hard and it went all wacky. I was going to backup my phone the next day, because I didn't have enough space, but now I couldn't. I can't through iCloud, because I can't navigate my phone, and I can't through my Mac, because I can't press the "Trust This Computer?" button. Any other ways to back it up?