Well the only other tank I have is the 10 gallon but it is just starting to cycle. It probably wouldn't be good to out them in a newly set up tank.
When I breed fish, the spawning tank is not the same as the holding tank. My fish are kept by gender in separate holding tanks that are set up for long term holding with filter, gravel, what have you. My spawning tanks are all newly set up bare tanks ( with danios, there would be a layer of marbles on the bottom) with new clean water. The only thing "cycled" that ever needs to go into this tank is the sponge filter and that doesn't have to go in until the fry are swimming.
I understand that you are somewhat "behind the 8 ball"now as your fish spawned and you are now trying to catch up but in the future, you may want to purposely spawn your fish so you have more control of your situation. Having multiple sponge filters running in your holding tanks all the time allows you to remove one and use it in your fry tank(s) when necessary.
What you can do once you get your sponge filter(s) is to empty the 10 if it has not finished cycling and add the fry and your 5 gals of water into the 10 gal, start up the sponge filter and get some beneficial bacteria from some gravel from your established tanks or a filter cartridge and add it to this tank. This will seed the tank and help keep ammonia somewhat under control. Since you will not be feeding high amounts of food at first and will be doing water changes on a frequent basis, you should be able to maintain high water quality until the filter bed really gets established. Danio fry are better off (IMO) in a bare tank so that they can find their food easier. Using live plants as a source for infusoria is a good way to avoiding over feeding at the start. I used bunch plants like Anacharis, Cabomba, etc, so that there were many places that the infusoria could be on the plants. You only want to put the fry into a decorated tank after they are eating foods where they, say, come to the surface when you feed them or go to a certain spot because they know you will be feeding them there. Until then, the less stuff in the tank, the better. You also want to not use any other type filtering other than a sponge until the fry are big enough to swim away out of any current that may be present from HOB or canister filters.
Hope this helps