I changed the fuel hose and now the gs500e cuts out in gear or with throttle applied.

I think maybe the hose is too narrow or maybe it is finicky how it is routed.  Now sure but wanted to ask here.

It was working fine before I changed the fuel hose but then the fuel hose split.

Which fuel hose ?. Tank 'on' to vac petcock 'on'?.  Theres no pump and it relies on gravity.. so if youve routed it like the water trap under your kitchen sink then it wont flow right.  And just to point out the obvious.. you havnt maybe left the tap on the tank half way open/ closed or sonething like that ?. The flat head groove should be at 12 and 6 o clock "|" not like "/" or something..
Another thought is to check you haven't dislodged the vacuum hose from petcock to carby as the tap relies on this to allow flow through..  switch to prime for 20 seconds to allow the bowls to fill after correcting whatevers wrong . Then back to "on" and start..

Did you use the ON/OFF Valve @the Petcock? (under tank) And if so, is it in the correct position now?

Here is an example of the problem.

Throttle stops the engine.
Putting the choke on helps keep the engine running.
With the choke on and minimal revs and careful application of the clutch the engine can be put into first gear however too much load on the engine results in the engine stopping.  A slight incline.  On that note this bike is heavy pushing it up my drive way is such a pain.

Also petrol has leaked or evaporated from the engine since I made this thread 3/4 of a tank.

What do you folks think?

you probably use non-oem hose cut to fit. look for a pinch In the line

Did you mix up on and reserve lines or let the tank get below reserve level but haven't switched over?
Otherwise other suggestions of tank petcock or pinched line sound like good options to explore.
You can test fuel delivery by putting the petcock on prime and opening the carb drain screw. That will rule out the fuel line.

I read the latest PO post to say he's lost 3/4 of a tank of fuel due to leaking or evaporation??? Is that right??? 

There's no way that amount of fuel will evaporate, so it has to have leaked somewhere.

If you don't have a bunch of fuel under the bike, it means it's likely to be in the crankcase.

I'd be smelling the dipstick if I were you and if it smells like fuel, you will need to do find/fix the fuel leak and then do an oil change ASAP before you find the fuel washes the oil away from bearings etc. and does some damage. Smell inside the crankcase as well, fuel will sit on top of oil so you should be able to smell the difference.

Someone's comment above around having the lines the wrong way round would certainly cause a leak if the vacuum operated fuel tap is letting fuel out instead of turning it off. If fuel can go down the vacuum line it will go into the carb and then straight into the cylinders etc.

I hope I'm wrong, but losing 3/4 of a tank of fuel would have my eyes bulging!

I'm not sure how the GS500 intake system works but I'm guessing it's also possible that some of that fuel went into the airbox as well?

With vacuum line taking in fuel you will have fuel in the cyls and then crankcase, likely very little will be in the airbox.
If the floats were overflowing you will get most of it in the airbox and the airbox will drain to the ground on the right side hose with that little cap on it but if that hose was missing, it comes out the left side on top and rear of the motor.
Either way find it and fix it, its pretty much a must fix now situation.
Cool.
Buddha.

I put it on idle for 10-15 minutes with the choke on until it finally revved high.  A bit more idle time and then I was able to open the throttle without fueling problem.  Went for a ride to fill the tyres and get petrol.  No issues on the ride.

My theory is there was air in the fuel line or something and it needed to idle for a while to move the air or something.