How to fix the iCloud thing?

So I want to change my iCloud account but it's stuck on another account that I don't know the password to. The only option it has is to sign out of that account but to sign out I also have to turn off find my iPhone but to do that I need the password. So how can I just delete the account that's on there without losing any pictures and stuff?

Have you actually tried to contact Technical Support? Maybe I'm just silly but that would be the 1st thing I would do as a person using their Brain.