Is there a synonym for the 'every x minutes' construct? The phrase I want to rephrase is 'the system generates a command every x minutes'.
You could use the word intervals:
The system generates a command at five-minute intervals.
Wordnik shows one definition of interval is:
interval (n.) The amount of time between two specified instants, events, or states.
Words like hourly, daily, weekly could serve as one-word synonyms for that construction in some cases, but they're much more specific units than you seem to be looking for.