Well, let me say that while I don't grow moss as a hobby I end up growing moss as a side-line

What I mean by this is I don't know the exact answer to your questions however I do know what happens in my tank. I run a bank of 4 48" t5 flourescents and the moss is about 20" away. That should equate to approx 750 FCs of light. You could achieve that easily with a large compact florescent bulb from Home Depot (say something in the 20-30 watt size). Yes your 5-gallon should work (I don't have personal experience but what I do know is the higher the humidity, the better. If you close the top, you'll need to "vent" the tank daily to allow fresh air in. The best way is a tiny 12-volt fan running constantly inside the tank with a piece of glass on top. Leave the glass on all the time except when you water the moss. Please understand, this is all a guess on my part, but this is what I would start with. If you collect the moss in the woods, it's free, so nothing's lost if mold takes over. If mold takes over, it means you need more ventilation (or air circulation).
My large tank has one 3" fan running 24/7 to circulate air. It has another through-wall fan I run approx 3 times a week (or when I remember) to bring fresh air into tank. If your 5-gal is sealed, then a 3" 12-volt fan should be fine. See
Coralife 3-1/8" Cooling Fan Kit This is the fan(s) I use. I have 4 of them right now and like them a lot.