I have a 2004 Gs500 and for some reason recently when the engine hits around 5000 rpm it makes this atrocious buzzing noise, if you lower the rpm its barely noticable and if you raise it it doesn't seem to be so bad as well. It still makes the sound when in neutral and stopped. And this may be unrelated but I am getting horrible gas mileage recently as well (around 37.5 mpg.) other than that the bike runs fine. Any ideas on what this might be would be appreciated, and knowledge about whether or not I should stop using it would be helpful.

Up front o the gas tank, there should be a rubber peice between it and the frame. If there is not, invent one.

Check all your mounting bolts. (engine)

Check your air filter, intake boots, and float needles. I'll bet on the float needles being shot, or poor float height.

i had a wierd buzzing noise similar to what I think you have, at just the right RPMs it buzzes, over or under and it doesn't? Check your windscreen, see how tight those top 2 screws are, if they are not tight, tighten them and see if it helps any.

My wind screen makes a buzzing sound at a certain rpm, do what svttuckf100 said and check it. I would check it by grabbing the windscreen while your hear the buzz.

If that isnt it, check your brakes -- did you buy new ones and replace them? I had to use the old silencers because I forgot to buy new ones that fit the new brakes. so once in a while it sounds like there is something being electrocuted within proximity

my guess it is one of the three rubber tank mount points.   Mine does it if I don't have the (backyard replacement rubber tubing) front tank mount installed.