Zoran,
Here is a link to MusicCity's excellent website, scroll down to the bottom for his essay's on thinning, cleaning and other airbrush and painting related tips and tecniques. This might not be necessary, but he offers good advice and shows that it isn't as black magic as it might seem to people.
If it's any consolation, my Badger 100LG didn't come with instructions. Well, it did, but it was generic and had more to do with airbrushing techniques, and not cleaning and repair.
Airbrushes are very easy tools, really. Here is an exploded parts view for the C-5. It's probably all one needs to reassemble the airbrush:
The wrench will be for loosening/tightening the nozzle, at least it is for my Badger. I use bee's wax on the threads to eliminate any air leaking around the threads.
I do caution using pliers and strength to tighten or loosen any part on an airbrush. It might be metal, but the parts do tend to be delicate. Especially any of the internal hollow parts, and pliers can crush things very quickly (ask me how I know!)!
Compressors are even easier! Use teflon tape (cheap at any hardware store) on any threads that connect regulator to compressor and hose to regulator. Hopefully Bear Air sent all the bits that you need. There should be a female connection on the compressor, or perhaps a male to male fitting already in place. The regulator will screw onto that, and if you look at the pic on the website, you'll see another male tp male connector that screws into the regulator. That is where you will put the hose, with the other end attaching to the airbrush.
Since you use acrylics, you will have a pretty easy time of cleaning. Use Windex (or other ammonia based window cleaner) to wash out the airbrush. Back flush at low pressure by holding a rag over the tip and carefully spraying. The back pressure will flush out any remaining paint into the cup and cause bubbles. I follow up with a good flushing using distilled water (you do NOT want mineral buildup inside the airbrush body!), and pull the needle to ensure that the needle is free of paint, and I wipe down with some lube (you can buy glycerin at the local drug store, enough to last your lifetime) on the front third of the needle. I also wipe glycerin in the color cup. I find it helps that it helps with the cleaning by putting a layer on the metal. It doesn't interfere with the Tamiya paints (acrylic paint retarder is mostly glycerin).
I'm sure you already know most of this stuff, but repeating it certainly does no harm. Give us a shout if you have any more questions. There are plenty of experts on this website!
Take your time, and don't lose patience. You'll do fine!