The optimization process and recommendations:

1. 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:

ALTER TABLE `tableb` ADD INDEX `tableb_idx_columna_columnb` (`columnA`,`columnB`);
ALTER TABLE `tablec` ADD INDEX `tablec_idx_id` (`Id`);
ALTER TABLE `tabled` ADD INDEX `tabled_idx_id` (`id`);
ALTER TABLE `tablee` ADD INDEX `tablee_idx_id` (`Id`);

The optimized query:

SELECT
        tableb.columnA,
        tableb.columnB,
        tablec.id,
        tabled.id,
        tablee.id 
    FROM
        tableA tableA 
    LEFT JOIN
        tableb tableb 
            ON (
                (
                    tableb.columnA = tableA.id
                ) 
                OR (
                    tableb.columnB = tableA.id
                )
            ) 
    LEFT JOIN
        tablec tablec 
            ON tablec.Id = tableb.columnA 
    LEFT JOIN
        tabled tabled 
            ON tabled.id = tableb.columnB 
    LEFT JOIN
        tablee tablee 
            ON tablee.Id = tableb.id