I have been using the */n syntax for the minute field for some time now to run a cron task every “n” minutes starting at the top of the hour.

What I did not realize is that

*/5

is actually equivalent to

0-59/5

which basically means: run every 5 minutes starting at the top of the hour (0).

So if you would like to run every 5 minutes starting at 2 minutes after the hour you would simply specify

2-59/5

Other examples:

5-59/15 run at 5, 20, 35, 50 minutes

1-59/2 run every 2 minutes starting at 1 minute after the hour