Good to hear about the dog. Poor thing. How can people do that to an animal?
I'm sorry if I misunderstood but is the tank you have the crab, gourami and neons in a 3 gallon? This isn't realy big enough so, as soon as you've set up the 5 gallon, move them all into that. Move all the gravel from the current tank into it, along with the heater and whatever filter you are using on the 3 gallon. If the 5 gallon has a filter of its own, run both. In about 2 weeks, take off the filter from the 3 gallon and just leave the 5 gallon's filter running (on the 5 gallon). This will ensure all the good bacteria from your currently set-up tank have had a chance to establish themselves in the 5 gallon.
About setting up the tank with gravel etc. Yes, that does work in the sense that it introduces the good bacteria and enables them to colonise the new tank. However, with no fish in the tank, there is no ammonia. Ammonia is the good bacteria's food. Basically, unless you were adding pure ammonia or fish food (when there were no fish in just after you put in the old gravel), the bacteria would have starved. So they wouldn't be doing their job once you added fish. Depending on how long you left them without food, it could take some time for the colony to build up enough again to sustain all the fish you have in this tank. The fact that it is tiny, also, means the waste accumulates much quicker as well. Also, if you cleaned the gravel/plants with tap water, most of the bacteria would have been killed by the chlorine in the water - so that puts an end to that plan.
Sorry I can't do much for you as far as reccomeding a book. I've read many but, to be honest, no single book contains all the information you need in enough detail. Most books cover cycling etc in some form but only a few realy delve deep into it and, even then, things are missed out. The best advice I can give as far as this is concerned is to use many sources. Read as many books as you can on this and other aspects of fish-keeping, search the internet, use this forum and ask questions - no matter how silly you may think they are, they may turn out to be a fish-saver.
In time, your accumulated knowledge and your own experiences will mean you are aware of the basics (though you already are aware of most of it as far as I can see) but you'll find you can still never do quite enough research on anything in this hobby. You realy do learn something new every day
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Good luck with everything and good luck to the dog too. Keep us updated.