For T5, coming from landside it would be about 37 minutes before departure - assuming you have got checked-in status in MMB/the App - since a quick scan is all that is needed and the boarding pass will be spat out in seconds. This is in order to clear T5 Ready to Fly by the 35 minute cut off. If you don't have have checked in status (in which case you wouldn't see this message as far as I know) then it would be before check-in closes, 60 or 45 (short haul) minutes before travel (and allegedy 20 minutes at LCY). If you were seeing this message at an out station like ZRH (or even connecting into T3) and you managed to get airside, it could be done airside at the gate.
So 70 minutes is overkill really.