Skip the old tank water... There's very, very little bacteria in it. Not enough to even make a noticeable difference. You would just be adding nitrates to the tank.
I would use your old filter from the 5g and run it on the new tank. Because the old filter is cycled this will hold your cycle till you can get the new filter to cycle(takes around a month). Test every day for a little bit after setup to ensure there is no spikes in parameters.
I wouldn't reuse the old substrate either. Like water, it doesn't hold much bacteria and can Barbour nitrates. If you really want to use it again, clean it first.
Hope this helps