Well, me being a fool and a noob, bought a bike that would barely start, and couldn't really ride, just cause the price was right. It's a '92 Suzuki GS500E.   The next day it wouldn't even start.  I cleaned the carbs and put new plugs in but it still ran like crap.  So I emptied the gas tank and refilled with new gas (I need to clean it out sometime, there's rust everywhere).  I changed the oil 'cause it was thin and smelled like gas.  I also let the air filter soak in gas for a couple hours and then dry over night.  Finally, I was able to take it out last night.

Worked awesome at high speeds (this is my first bike so high speeds for me is like 60 mph).  However, I seemed to be having fuel starvation problems unless I put the bike in prime.  However, if it was in prime, at low speeds every so often when I would pull up to a stop, the bike would die and not want to start until several seconds of cranking and opening the throttle wide.  I'm wondering if it's possible to flood the carbs by leaving it in prime and going low speeds?  However, when I put it on 'on' or 'reserve' it seems to have fuel starvation issues.  One other thing I noticed was that the previous owner had installed an inline fuel filter.  Seems kind of dirty.  I want to replace it (with another filter not a straight hose because of the rusted gas tank problem) however, I'm not really sure what kind of filter people have been having success with here.  If there's a common filter or two that gives good results with our bikes, please point me in the right direction. 

One other thing, when draining the gas tank, the fuel only drained out the 'reserve' point of the in-tank petcock.  Is this normal?  Thanks in advance for your help all.  Although I haven't posted too many questions, the search tool has been invaluable about 50 times already getting this bike up and running.

Sounds like your going though what I did a few years ago. I myself was  new rider and had bought a 95' GS500...first bike ever. My friend talked me into, and I had bought it off of another friend, who had since bought it off of a few of my other friends, so I knew the bike history quite well. Only thing was they jerry rigged thing a million diffrent ways so they could just ride with out putting any serious money and time into it. It ran, but I didn't ride it untill it was fix, and didn't show it to anyone untill I was happy with it. My friends said it was lost cause but with alot of money and efforct, cold nights and long days I got it done. The carb was so messed up, some one had put blue gue on the valve cap because it was broke, (rahter than get a new one), but folded up aluminum under the valve springs to give them more tenchion because I guess it was not running right, the bike had been crash and the fairings were broke in so many places. Well I bought all new parts for the carb. I started it up and it wouldn't idle, and when I got past 5,000rpm it reved up to 8,000 or so and wouldn't come down. Took me forever to get it fixed..had to get it rejeted. Rather than buy new fairings. I re-fiberglassed the whole things, done body filler on the cracks, chips, and holes, (by the way the fairings were totally held together with vairous bolts, screws, and bailing wire.) Feather sanded it down, and then primed it, with 3 coats, then painted with two, one high gloss, Ordered all the fairing bolts I needed. Needless to say, once finished which was about 5 months. I took it out on it's first spin, went down town and ppl didn't even know the bike, they thought I bought a new one. Even the previous owners couldn't believe it. But it was totally worth it.

The fuel starvation problems are common. Since PRI helps it's probably a petcock issue in your case, though the fuel filter may also contribute.

That PRI does not work right in low fuel demand situations hints towards a malfunctioning float valve (stuck float or damaged needle): The carbs overflow.

I know the symptom of the bike dying when decelerating hard from a time when I ran mine with float heigth way off (with fuel level way too high in the bowls.)

When I cleaned the carbs, I checked the needle and it was good.  When I put it back I guess its possible that I got it stuck.  I'll have to try Kerry's float valve trick.  Although if it does need adjusting that'll be fun.

Oh also, I need a new gas cap.  the guy before me lost the key and carved it out, so all it takes is a screwdriver to open it.  Is there a cheaper place to get one besides OEM.  It was over $100.