Does anyone have any idea how I could create a new logfile every n minutes?

Most decent Unix systems provide you with a newsyslog utility which runs from cron or a workalike which does exactly what you want, and often much more. Any decent implementation isn't limited to working with syslog logfiles.

If you're running on Windows or something ne Unix ... well ... I honestly don't know. You'd need to post more about what sort of logfile you're rotating, any specifics about rotating it, etc. before we could be more detailed in our answers.