I was trying to figure out how the camera works, as I was unable to release the shutter, thus I thought that I was missing some point and was even going to write emails to all the Moskva-5 sites in my bookmarks.
But during the thorough cleaning of the camera (which included cleaning the bellows with the vacuum cleaner) I found out, that a lever, that I thought was ment as a lock for the lens, was indeed an auxiliary lever that was thought to push the actual shutter release lever on the lens body. The lever was out of it's place, and it did cost me around 15 minutes to figure out how to put it back again in place... until I found out that you can simply crease the bellows, work and revert it to it's original state with just a slight kick with the fingers from the inside.
I strongly suggest doing the same as me if you have got one of these cams from the former Soviet Union, as they can have lots of dirt, even dead bugs (I found a dead moth trapped in the bellows).
A good idea is to unmount the upper case that holds the viewfinder and the rangefinder mechanism. Opening it is very easy; there is only one screw that needs a screwdriver, that's the screw on the film advance wheel. Then simply unscrew the rangefinder windows and pull the release button. That's all. Pretty simple. Now you can clean the rangefinder and the viewfinder lens, remove the old grease and the dust.
Unmounting the lens is also pretty simple, but you will need an ultra-fine precision screwdriver. There are 4 micro-screws on the outer border of the focusing ring. Once removed, you can take the outer part of the lens out. I found out that there is plenty of dirty grease in this screw, I haven't removed all yet, tough.