Would adding a find command to cron work for you?
find /path/ -type f -mtime +5 -name '*.log'
You can layer on extra things to find just the files you want. -mtype is the date-limiting portion which finds files last modified over 5 days ago. You can change this to just look at creation or even access times (if you're not using noatime on your fs)
When you're getting the right files, just stick -exec rm {} \; on the end. You could use -delete but that will crumble if you have too many files being deleted at once. Only do this once you're sure!
When you want to schedule it, su into the right user account (the person who owns the files) and then run crontab -e. You can then write out the command and when you exit, it'll run at the schedule you set. You can read more about cron here:
https://help.ubuntu.com/community/CronHowto