Delete data from huge InnoDB table from MySQL Master and Slaves
Here are some things you should consider:
CONSIDERATION #1
Using DELETE FROM tbl ... LIMIT 5000 is not replication-safe because the  5000 rows being deleted may not be the same order or the same set of 5000 rows on a slave. See MySQL Documentation (Replication and LIMIT). Should a DELETE on a Master get interrupted, it has to rollback. In that event, it could be remotely possible that the number of times the DELETE FROM tbl ... LIMIT 5000 is called may not be the same. Extra calls of the DELETE on a Slave is not critical. Too few calls could be bad. This should not happen.
SUGGESTION : Make sure the row count for RTesAll is identical on the Master and all Slaves.
CONSIDERATION #2
Since you are running a Stored Procedure on the Master, the DELETE command will not begin its execution on a Slave until the completion of the DELETE on the Master and the DELETE command is posted in the Master's Binary Logs. With one Master and 4 Slaves (5 DB Servers), there are a certain of calls to DELETE multiplied by 5.
SUGGESTION #1 : You should add set sql_log_bin = 0; to the Stored Procedure
DROP PROCEDURE IF EXISTS PurgeOlderData;
DELIMITER $$
CREATE PROCEDURE `PurgeOlderData`(In StartDate DATETIME ,In EndDate DATETIME,In NoOfRecordsToDelete BIGINT,In TableName CHAR(50))
BEGIN
    SET sql_log_bin             = 0;
    SET @delete_counter             = 0;
    SET @table_name             = TableName;
    SET @number_of_records_to_delete    = NoOfRecordsToDelete;
    SET @start_date             = StartDate;
    SET @end_date               = EndDate;
    
    WHILE @delete_counter &lt; @number_of_records_to_delete DO
        SET @varSQL = CONCAT('DELETE FROM ', @table_name,' WHERE recordDate BETWEEN \'',@start_date ,'\' AND \'', @end_date ,'\' LIMIT 5000;');
        PREPARE stmt FROM @varSQL;
        EXECUTE stmt;
        DEALLOCATE PREPARE stmt;
        /*SELECT @varSQL;*/
        SET @delete_counter = @delete_counter + 5000;
    END WHILE;          
    SET sql_log_bin             = 1;
END $$
DELIMITER ;

to prevent all DELETEs from replicating. If you are deleting 611992998 rows, deleting every 5000 rows requires executing DELETE ... LIMIT 5000 122399 times (That's 611992998 / 5000 rounded up to next integer).
This will prevent having to write to the binlogs 122399 times.
SUGGESTION #2 : Run the Stored Procedure on the Master and Slaves at the same time.

This prevents replication lag
This gets rid of all the rows at the same time
This is best done during maintenance cycles or slow read times

CONSIDERATION #3
Make sure autocommit is enabled on Master and Slaves. Otherwise, all the deletes will pile up in the undo logs inside ibdata1 before either doing all the deletes at once as a single transaction or a huge rollback.
Give it a Try !!!