The latest version of WordPress supported by MemberMouse is:
NOTE about WP 5.3+ - WordPress 5.3.x was released on November 12th, 2019, and introduced an Administrative Email Verification Feature. We have identified an issue that will periodically occur (by default, every six months) with any version of the MemberMouse plugin. When the issue manifests, any Administrator logging in using the MemberMouse login page will be redirected to the Error Core Page (or the Member Home Page in WP 5.6) and the message "on=confirm_admin_email" will be appended to the URL in the browser address bar. Administrators encountering this can proceed to the WordPress Admin dashboard manually, by going to yoursite.com/wp-admin. We are working on a fix for this issue, to be included in a future version. If you encounter this behavior, you can restore normal function to the MemberMouse Login page by temporarily setting the WordPress login page as default from MemberMouse > General Settings > Other Settings, log out and back in again to verify your Administrative email address, and then reset the MemberMouse login page as default. If you have any questions, please feel free to contact our support team.
It is always best to have a current site backup before upgrading your version of WordPress. Your hosting provider should be able to assist you with securing a backup.
Downgrading to a Previous Version of WordPress
WordPress Release Archive