I have an 1986 550L and the best way to get it started is to push start it.
I own a 1979 GS 550L and regularly get 45 MPG, sometimes a bit more.
The V.I.N number on most bikes can be found stamped into the side of the headstock. Alternatively it may be stamped somewhere on the frame in that vicinity. Failing that, look under the tank and seat (possibly even on the underside of the tank or seat).
If the carbs have not been totally disassembled, they should not need "syncing". Most problems I encounter are from dirt or scud buildup. If you are reasonably handy, you can remove the float bowls, blow out all the jets , the main body, and reassemble them with the floats and needles in their orig positions. 9 times out of 10, this will work. If you do indeed have to adjust them, you will need a synching tool. I do not recommend the mercury type for a beginner because it's too easy to suck up the mercury. In the end, it's worth the heartache to spend a little dough and have a qualified professional diagnose and repair your problem.