How to improve query performance (using explain command results f.e.)

I'm currently running this query. However, when run outside phpMyAdmin it causes a 504 timeout error. I'm thinking it has to do with how efficient the number of rows is returned or accessed by the query.

I'm not extremely experienced with MySQL and so this was the best I could do:

SELECT
                    s.surveyId,
                    q.cat,
                    SUM((sac.answer_id*q.weight))/SUM(q.weight) AS score,
                    user.division_id,
                    user.unit_id,
                    user.department_id,
                    user.team_id,
                    division.division_name,
                    unit.unit_name,
                    dpt.department_name,
                    team.team_name
                FROM survey_answers_cache sac
                    JOIN surveys s ON s.surveyId = sac.surveyid
                    JOIN subcluster sc ON s.subcluster_id = sc.subcluster_id
                    JOIN cluster c ON sc.cluster_id = c.cluster_id
                    JOIN user ON user.user_id = sac.user_id
                    JOIN questions q ON q.question_id = sac.question_id
                    JOIN division ON division.division_id = user.division_id
                    LEFT JOIN unit ON unit.unit_id = user.unit_id
                    LEFT JOIN department dpt ON dpt.department_id = user.department_id
                    LEFT JOIN team ON team.team_id = user.team_id
                WHERE c.cluster_id=? AND sc.subcluster_id=? AND s.active=0 AND s.prepare=0
                GROUP BY user.team_id, s.surveyId, q.cat
                ORDER BY s.surveyId, user.team_id, q.cat ASC

The problem I get with this query is that when I get a correct result returned it runs quickly (let's say +-500ms) but when the result has twice as much rows, it takes more than 5 minutes and then causes a 504 timeout. The other problem is that I didn't create this database myself, so I didn't set the indices myself. I'm thinking of improving these and therefore I used the explain command:

---

---

I see a lot of primary keys and a couple double indices, but I'm not sure if this would affect the performance this greatly.

EDIT: This piece of code takes up all the execution time:

$start_time = microtime(true);
$stmt = $conn->query($query); //query is simply the query above.
while ($row = $stmt->fetch_assoc()){
    $resultSurveys["scores"][] = $row;
}
$stmt->close();
$end_time = microtime(true);
$duration = $end_time - $start_time; //value typically the execution time #reallyHigh...

So my question: Is it possible to (greatly?) improve the performance of the query by altering the database keys or should I divide my query into multiple smaller queries?

The EXPLAIN result is showing signs of problem

Using temporary;using filesort: the ORDER BY needs to create temporary tables to do the sorting.

On 3rd row for user table type is ALL, key and ref are NULL: means that it needs to scan the whole table each time to retrieve results.

Suggestions:

1. add indexes on user.cluster_id and all fields involved on the ORDER BY and GROUP by clauses. Keep in mind that user table seems to be under changein database (cross database query).
2. Add indexes on user columns involved on JOINs.
3. Add index to s.survey_id
4. If possible, keep the same sequence for GROUP BY and ORDER BY clauses
5. According to the accepted answer in this question move the JOIN on user table to the first position in the join queue.
6. Carefully read this official documentation. You may need to optimize the server configuration.

PS: query optimization is an art that requires patience and hard work. No silver bullet for that. Welcome to the fine art of optimizing MySQL!