The optimization process and recommendations:

1. Avoid Selecting Unnecessary Columns (query line: 2): Avoid selecting all columns with the '*' wildcard, unless you intend to use them all. Selecting redundant columns may result in unnecessary performance degradation.
2. Create Optimal Indexes (modified query below): The recommended indexes are an integral part of this optimization effort and should be created before testing the execution duration of the optimized query.
3. Replace In Subquery With Correlated Exists (modified query below): In many cases, an EXISTS subquery with a correlated condition will perform better than a non correlated IN subquery.

Optimal indexes for this query:

ALTER TABLE `table1` ADD INDEX `table1_idx_field4` (`field4`);
ALTER TABLE `table2` ADD INDEX `table2_idx_field3_field1` (`field3`,`field1`);
ALTER TABLE `table3` ADD INDEX `table3_idx_field6_field5` (`field6`,`field5`);

The optimized query:

SELECT
        * 
    FROM
        table1 a 
    JOIN
        table2 b 
            ON b.field1 = a.field1 
    WHERE
        b.field3 = 1531 
        AND a.field4 = 0 
        AND EXISTS (
            SELECT
                DISTINCT 1 
            FROM
                table3 
            WHERE
                (
                    table3.field6 = 172
                ) 
                AND (
                    a.field5 = table3.field5
                )
        )