How to transfer pictures on iphone 4 to iphone 5 without using itunes?

I'm getting my moms old iphone 4 because mine broke. She told me i can't sync it to my laptop until i find a way to transfer all of the pictures on her old phone to her new one and we can't do it through itunes because the laptop which the old iphone was synced on is broken. Any Ideas?

Added (1). Around 3000 photos so any uploading is not an option.lol

Upload them to an online storage site.