U can call times above 5000, but below 10,000 when cruise is above 10,000ft... and if cruise is below 10,000 you can call upon reaching cruise altitude.
You are required to call when ground delays are expected to exceed 15 minutes, or gate delays in excess of 10 minutes. There is nothing in the book that says you can not make these calls as a CA. It does specifically say that you may not confirm gates or reservations for pax. though.
If you are doing it in a way that is ok in the FOPP, the faa won't get mad at you... they approved it.
At least at cjc it's this way
Bingo!