Ya encontré la solución y se debe agrupar los resultados con HAVING
Código SQL:
Ver originalFROM
posts Posts
INNER JOIN fields_posts FieldsPosts ON (
FieldsPosts.VALUE IN ('1', '5')
AND Posts.id = (FieldsPosts.post_id)
)
WHERE
(
Posts.STATUS = 'active'
AND Posts.TYPE = 'Post'
)
GROUP BY
Posts.id
HAVING
COUNT(DISTINCT FieldsPosts.VALUE) = 2