My aim is to do exactly what a LEFT OUTER JOIN intends to do using the 4th venn diagram: SQL Diagrams:
You current query is basically doing an INNER JOIN because of the consultant_id = 5 on the WHERE clause. I believe you actually want to use:
SELECT *
FROM consultant_memberships m
LEFT OUTER JOIN consultant_memberships_list l
ON m.`id` = l.membership_id
AND l.consultant_id = 5
WHERE l.membership_id IS NULL;
See SQL Fiddle with Demo