Changed id & password will not work with iCloud

I have recently changed my Apple id and password.This works fine with everything except iCloud. iCloud keeps displaying my old Apple id and asking for a password. I enter my new password which it will not accept, neither will it accept any of my old passwords. If I click on "forgot"and enter my old Apple id to get a new password I receive a message telling me that my old Apple id is not a correct Apple id. I am using iOS Yosemite 10.10.5.

I cannot get out of this loop. How do I get into iCloud to reset it to my new Apple id & password?