I have another option, if you are ok using the stock "automated cron" (aka poor man's cron) module that comes with drupal, which I'm assuming based on the question, you are.
You can set the interval for cron using settings.php.
In drupal 7
$conf['cron_safe_threshold'] = 300;
In drupal 8+
$config['automated_cron.settings']['interval'] = 300;
Obviously, do to the nature of the way the Drupal automated cron works, this wouldn't garentee the cron to be run every 5 minutes, but instead would be run on the next visit to any page that hit Drupal after 5 minutes have pasted since the last run. This is also true with the standard settings but at larger intervals obviously. This does mean if you do have edge caching like varnish in front or simply little traffic to the site, this may not be ideal.
Also, given the setting is set via settings.php, the drop down will no longer show the correct value and may be misleading to another developer or administrator.