I changed my apple ID but my laptop still has me logged into the cloud w/my old apple ID

I changed my apple ID but my laptop still has me logged into the cloud w/my old apple ID. It will not let me log out of my old account without entering the old pw. The password doesn't work, my birthday does not work to verify it, and the email address linked to "retrieve password" is a former job. I just need to log out of iCloud so I can log back in with my new apple ID.