How do I make cron run something every "N"th minute, where n % 5 == 1?
1-56/5 * * * * /my/script
This should work on vixiecron, I'm not sure about other implementations.
Use your first schedule:
*/5 * * * * /my/script
And add this to the start of your script:
sleep 60
(Yes, this is a joke)