You can also add to /etc/mysql/my.cnf (in Debian, google for the rest of the distributions) the following
expire_logs_days = 5
in order to keep only the last 5 days binary logs.
I'm almost sure that the normal user doesn't need then binary logs (except the case when they use master-slave replication or they know what they are doing), so why not disabling them completely? (mysql say that only 1% of the server speed is lost when bin logs are active but still that's something)
Comment log-bin directive in the /etc/mysql/my.cnf - Debian
Also, why not removing the binary logs (except the last one) with:
rm -rf file.XXXX
I didn't read anywhere that MySQL is keeping any "an eye" on those files...