I'm trying to optimize the following query without success. Any idea where it could be indexed to prevent the temporary table and the filesort?

EXPLAIN SELECT SQL_NO_CACHE `groups`.*
FROM `groups`
INNER JOIN `memberships` ON `groups`.id = `memberships`.group_id
WHERE ((`memberships`.user_id = 1) 
  AND (`memberships`.`status_code` = 1 AND `memberships`.`manager` = 0))
ORDER BY groups.created_at DESC LIMIT 5;`

+----+-------------+-------------+--------+--------------------------+---------+---------+---------------------------------------------+------+----------------------------------------------+
| id | select_type | table       | type   | possible_keys            | key     | key_len | ref                                         | rows | Extra                                        |
+----+-------------+-------------+--------+--------------------------+---------+---------+---------------------------------------------+------+----------------------------------------------+
|  1 | SIMPLE      | memberships | ref    | grp_usr,grp,usr,grp_mngr | usr     | 5       | const                                       |    5 | Using where; Using temporary; Using filesort | 
|  1 | SIMPLE      | groups      | eq_ref | PRIMARY                  | PRIMARY | 4       | sportspool_development.memberships.group_id |    1 |                                              | 
+----+-------------+-------------+--------+--------------------------+---------+---------+---------------------------------------------+------+----------------------------------------------+
2 rows in set (0.00 sec)


    +--------+------------+-----------------------------------+--------------+-----------------+-----------+-------------+----------+--------+------+------------+---------+
| Table  | Non_unique | Key_name                          | Seq_in_index | Column_name     | Collation | Cardinality | Sub_part | Packed | Null | Index_type | Comment |
+--------+------------+-----------------------------------+--------------+-----------------+-----------+-------------+----------+--------+------+------------+---------+
| groups |          0 | PRIMARY                           |            1 | id              | A         |           6 |     NULL | NULL   |      | BTREE      |         | 
| groups |          1 | index_groups_on_name              |            1 | name            | A         |           6 |     NULL | NULL   | YES  | BTREE      |         | 
| groups |          1 | index_groups_on_privacy_setting   |            1 | privacy_setting | A         |           6 |     NULL | NULL   | YES  | BTREE      |         | 
| groups |          1 | index_groups_on_created_at        |            1 | created_at      | A         |           6 |     NULL | NULL   | YES  | BTREE      |         | 
| groups |          1 | index_groups_on_id_and_created_at |            1 | id              | A         |           6 |     NULL | NULL   |      | BTREE      |         | 
| groups |          1 | index_groups_on_id_and_created_at |            2 | created_at      | A         |           6 |     NULL | NULL   | YES  | BTREE      |         | 
+--------+------------+-----------------------------------+--------------+-----------------+-----------+-------------+----------+--------+------+------------+---------+


     +-------------+------------+----------------------------------------------------------+--------------+-------------+-----------+-------------+----------+--------+------+------------+---------+
| Table       | Non_unique | Key_name                                                 | Seq_in_index | Column_name | Collation | Cardinality | Sub_part | Packed | Null | Index_type | Comment |
+-------------+------------+----------------------------------------------------------+--------------+-------------+-----------+-------------+----------+--------+------+------------+---------+
| memberships |          0 | PRIMARY                                                  |            1 | id          | A         |           2 |     NULL | NULL   |      | BTREE      |         | 
| memberships |          0 | grp_usr                                                  |            1 | group_id    | A         |           2 |     NULL | NULL   | YES  | BTREE      |         | 
| memberships |          0 | grp_usr                                                  |            2 | user_id     | A         |           2 |     NULL | NULL   | YES  | BTREE      |         | 
| memberships |          1 | grp                                                      |            1 | group_id    | A         |           2 |     NULL | NULL   | YES  | BTREE      |         | 
| memberships |          1 | usr                                                      |            1 | user_id     | A         |           2 |     NULL | NULL   | YES  | BTREE      |         | 
| memberships |          1 | grp_mngr                                                 |            1 | group_id    | A         |           2 |     NULL | NULL   | YES  | BTREE      |         | 
| memberships |          1 | grp_mngr                                                 |            2 | manager     | A         |           2 |     NULL | NULL   | YES  | BTREE      |         | 
| memberships |          1 | complex_index                                            |            1 | group_id    | A         |           2 |     NULL | NULL   | YES  | BTREE      |         | 
| memberships |          1 | complex_index                                            |            2 | user_id     | A         |           2 |     NULL | NULL   | YES  | BTREE      |         | 
| memberships |          1 | complex_index                                            |            3 | status_code | A         |           2 |     NULL | NULL   | YES  | BTREE      |         | 
| memberships |          1 | complex_index                                            |            4 | manager     | A         |           2 |     NULL | NULL   | YES  | BTREE      |         | 
| memberships |          1 | index_memberships_on_user_id_and_status_code_and_manager |            1 | user_id     | A         |           2 |     NULL | NULL   | YES  | BTREE      |         | 
| memberships |          1 | index_memberships_on_user_id_and_status_code_and_manager |            2 | status_code | A         |           2 |     NULL | NULL   | YES  | BTREE      |         | 
| memberships |          1 | index_memberships_on_user_id_and_status_code_and_manager |            3 | manager     | A         |           2 |     NULL | NULL   | YES  | BTREE      |         | 
+-------------+------------+----------------------------------------------------------+--------------+-------------+-----------+-------------+----------+--------+------+------------+---------+