[root@ns165 ~]# cat /usr/local/directadmin/conf/mysql.conf
user=da_admin
passwd=xxxxxxxxxxx

Please do not just delete them in the OS.

You need to let mysqld do that for you. Here is how mysqld manages it:

The file mysql-bin.index keeps a list of all binary logs mysqld has generated and auto-rotated. The mechanisms for cleaning out the binlogs in conjunction with mysql-bin.index are:

PURGE BINARY LOGS TO 'binlogname';
PURGE BINARY LOGS BEFORE 'datetimestamp';
These will clear all binary logs before the binlog or timestamp you just specified.

For example, if you run

PURGE BINARY LOGS TO 'mysql-bin.000223';
this will erase all binary logs before 'mysql-bin.000223'.

If you run

PURGE BINARY LOGS BEFORE DATE(NOW() - INTERVAL 3 DAY) + INTERVAL 0 SECOND;
this will erase all binary logs before midnight 3 days ago.

If you want to have binlog rotated away automatically and keep 3 days woth, simply set this:

mysql> SET GLOBAL expire_logs_days = 3;
then add this to /etc/my.cnf

[mysqld]
expire-logs-days=3
and mysqld will delete them logs for you

SHOW SLAVE STATUS\G

This is critical. When you run SHOW SLAVE STATUS\G, you will see two binary logs from the Master:

Master_Log_File
Relay_Master_Log_File
When replication has little or no lag these are usually the same value. When there is a lot of replication lag, these values are different. Just to make it simple, choose whatever Relay_Master_Log_File is, and go back to the Master and run

PURGE BINARY LOGS TO 'Whatever Relay_Master_Log_File Is';
That way, replication is not interrupted.

Give it a Try !!!