Just look for stuff like oil leaks, behind the clyinder heads and on the side cases and listen for clanging noises from the enigne (timing chain or bearing will cause this). The GS500E in general are good bike and great for beginners. The bike is same today as it was in 1987 so parts are everywhere. The engine is bulletproof and rides great.
I recommend radial tires, stock is bias-ply and were good but I went to radials and it made a big differance.
Mine has almost 35,000 miles on it and is starting to show some ware, I've been doing track days the last 3 years so the usage is not quite normal.
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Team Pro-Motion Safety Director/Coach #23