My aim is to do exactly what a LEFT OUTER JOIN intends to do using the 4th venn diagram: SQL Diagrams:
Use
SELECT *
FROM consultant_memberships
LEFT Outer JOIN consultant_memberships_list
ON consultant_memberships_list.membership_id = consultant_memberships.`id`
and consultant_memberships_list.consultant_id = 5
where consultant_memberships_list.membership_id IS NULL;
The Where clause used before in your query "consultant_memberships_list.consultant_id = 5 " was neglecting the left outer join.