I recently bought a 1993 gs500e and I cannot figure out what is keeping it from starting. I cleaned the carbs, cleaned the gas tank, and changed the spark plugs. There is spark and the timing is correct. Previous owner said it kept backfiring and eventually wouldn't start. Please help

If you can, post a video. Not starting could be weak battery, clogged pilot jet, wonky idle screw, starter relay, starter itself, etc. The sounds it makes when trying to start is important. I.e. does it just click one, click rapidly, click and give a weak "ruuuuuuhhhhn" sound, click and give repeated starting sounds? Lots of potential issues - but capturing how it sounds when turning over can lend a lot of clues.

I have the battery hooked up to my car and the starting sound sounds normal. Where is the starter relay? Could that cause the backfiring problem?

Well, if you are getting a normal turnover sound it likely isn't the relay. Are you getting spark from your spark plugs?

It has spark and two new spark plugs. When I pull the plugs after cranking it, they are wet. Why would i have spark on the outside and not the inside of the engine? The previous owner said it was backfiring a lot before he couldn't get it to start. (I hope that gives some kind of clue cause I am at a total loss.)

Backfiring, to my knowledge and others can correct me if I am wrong, usually means that fuel is detonating in the exhaust, rather than the cylinder. It means too much fuel, or a rich condition is being generated. I think there can be other causes as well, but that is usually the most common.

If you have wet plugs, that shows you are getting fuel into the cylinder, so that is good. I am going to assume that you have checked the idle screw and it isn't completely in or out? It is the big knob at the bottom-middle of the carbs.

You wouldn't have spark on the outside of the engine; but you can check to see if you have spark either via a spark plug tester or grounding it to the head of the engine. Just be careful, you are playing with live current if you do so - wear rubber gloves to be safe if you do that.

It has spark. Is it possible the valves could be out of adjustment enough that backfires and no-starts will occur? I am checking the valves now.