The optimization process and recommendations:

1. Avoid Calling Functions With Indexed Columns (query line: 17): When a function is used directly on an indexed column, the database's optimizer won’t be able to use the index. For example, if the column `Col5` is indexed, the index won’t be used as it’s wrapped with the function `LTrim`. If you can’t find an alternative condition that won’t use a function call, a possible solution is to store the required value in a new indexed column.
2. Avoid Calling Functions With Indexed Columns (query line: 18): When a function is used directly on an indexed column, the database's optimizer won’t be able to use the index. For example, if the column `Col1` is indexed, the index won’t be used as it’s wrapped with the function `LTrim`. If you can’t find an alternative condition that won’t use a function call, a possible solution is to store the required value in a new indexed column.
3. 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.

Optimal indexes for this query:

CREATE INDEX table1_idx_col1 ON Table1 (Col1);

The optimized query:

SELECT
        a.Col1,
        IsNull(a.Col2,
        '') Col2,
        IsNull(a.Col3,
        '') Col3,
        IsNull(a.Col4,
        '') Col4,
        IsNull(a.Col5,
        '') Col5,
        IsNull(b.Col2,
        '') bCol2 
    FROM
        Table1 a 
    LEFT OUTER JOIN
        Table2 b 
            ON LTrim(RTrim(IsNull(a.Col5,
        ''))) = LTrim(RTrim(IsNull(b.Col1,
        ''))) 
    ORDER BY
        a.Col1