The optimization process and recommendations:

1. Avoid OR Conditions By Using UNION (modified query below): In mosts cases, filtering using the OR operator cannot be applied using indexes. A more optimized alternative will be to split the query to two parts combined with a UNION clause, while each query holds one part of the original OR condition.
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. Use UNION ALL instead of UNION (query line: 24): Always use UNION ALL unless you need to eliminate duplicate records. By using UNION ALL, you'll avoid the expensive distinct operation the database applies when using a UNION clause.

Optimal indexes for this query:

ALTER TABLE `Table1` ADD INDEX `table1_idx_col2_col3_col5` (`Col2`,`Col3`,`Col5`);
ALTER TABLE `Table1` ADD INDEX `table1_idx_col2_col3_col4` (`Col2`,`Col3`,`Col4`);
ALTER TABLE `Table1` ADD INDEX `table1_idx_col1` (`Col1`);

The optimized query:

SELECT
        SUM(internal_agg_count) 
    FROM
        ((SELECT
            COUNT(*) AS internal_agg_count 
        FROM
            Table1 
        WHERE
            (
                Table1.Col2 = 'xyz' 
                AND Table1.Col3 = 'mnl' 
                AND Table1.Col5 = 'ijk'
            )) 
    UNION
    DISTINCT (SELECT
        COUNT(*) AS internal_agg_count 
    FROM
        Table1 
    WHERE
        (Table1.Col2 = 'xyz' 
        AND Table1.Col3 = 'mnl' 
        AND Table1.Col4 = 'efg')) 
UNION
DISTINCT (SELECT
    COUNT(*) AS internal_agg_count 
FROM
    Table1 
WHERE
    Table1.Col1 = 'abc')
) AS union1