I would drain 70-80% of the water out of the 5G before transporting,
and keep the filter media in the remaining tank's water.
Do not leave it in the filter.
It wouldn't hurt to clean it with used tank water
before putting it into the tank.

I would not transport them in the 5G tank.
Keep the frogs in a glad tupperware style container in a cooler to keep the maintained temp.
Make sure there are air holes for them to breathe.

2 hours should be fine to keep the colonies alive.

You can bring the old tank water with in a bucket if you want,
so there's less of a shock from the new water wherever you'll be filling up
the tank again.