(Yes, if AU is your destination, duty free is deliver to the gate, so you need to purchase it 90(?) minutes before flight time.)
Five hours is effectively four hours I suppose, so if you did not want to enter Singapore, you could visit the butterfly garden and orchid garden, take the skytrain past the Jewel waterfall, have a swim at the T1 aerotel (expensive for a family though), or just chill in the lounge if you have access (?).
It's easy enough to enter Singapore with the on-line SGAC (no fee - do not accidentally go to third party sites), so you could visit Jewel, or taxi/uber to East Coast for chill crab and black pepper crab, or Changi Village for more (better value) local food. Or just walk down to the staff canteens in the basements of T1 and T2.