I bought a 96 GS500e, it starts and idles fine but if you give it a little throttle it "bogs down" and dies.  In neutral, if you really nurse it up past ~5000 RPM it will hold the higher RPMs (it helps if the choke is on).  When riding, it wants to die at low RPM or when accelerating from a stop, but if you get it up past ~5000 RPM you can maintain speed.  I thought for sure it would be a bad pilot jet so I cleaned the carb and the pilot was clogged. I replaced it along with all of the o-rings.  I also replaced the intake boots.  I put it back together, same problem. I took the carb back apart, cleaned it again and still dies.   I don't even know where to go from here, any ideas?

Perhaps a petcock issue?

Could a petcock issue allow to both idle and run at high RPMs?

hmm, in re-reading, I'm not sure, I'd say petcock is actually wrong, didn't really understand the first time. Does it run fine over 5000? How's your needle set? Sounds like you're still lean in the pilot circuit. Try spraying starter fluid or wd40 around the boots to see if they're seated incorrectly. I'm not Buddha, by the way, this is just stuff to look at.

It "runs" over 5000, but I wouldn't say its happy.  I have only had it up there a couple of times because the bike is really by no means rideable.  In neutral, it will run over 5000 IF you can get it up past the low range of 1500~3000 without it dying.  The needle is clipped in the middle and there's no leak at the boots.  A bad pilot circuit does make sense, but I don't know what else to check.

I got nothing... Paging the Buddha, call for you at the front desk...