Kawasaki kx 125 2005 runs then cuts out

sounds like a clogged up fuel jets, you will need to clean the jets out and change the fuel filter.

Sounds like a failing ignition coil or trigger. If you let it cool for a long while it will closer to ten minutes and the plug is dark and fluffy then its weak spark. Check the coil ground and wire condition also.

sounds like a carb overhaul time as well as a fuel system flush

What kind of bike is it? If it's a moped i would recommend to clean your carb. Also shaking the fuel tank should help.

have you checked your idler screw on the side of the carb? if not it may be a blocked main jet, also check your air filter. try taking it out completely and running it. if it runs it may need replacing.

Pull the plugs, if they are black dry and sooty those cylinders are running too rich which may be why it's cutting out when you put the choke on, it's getting too much fuel.

If they are wet and smell of gas you have no spark to those cylinders.

If it's carbuerated, then your idle jets or main jets are possibly clogged if the bike has not been run in awhile.

Could also be the coil is not firing to those two cylinders, check for spark first then check compression.

Check your choke cable adjustment also to make sure it's working properly.

probly rite-the electrics are heating up from age--cud test each system--secure urself a clymer manual for proper procedure

This could be due to timing screw being incorrectly set
Locate gold timing screw on the carbrettta turn it clockwise only slightly till bike idles without choke on, Then when choke it on it should idle a touch higher.

first drain the carby, then set your air mixture screw 2 turns out, from the fully turned in position. The starting proceedure is as follows, when the engine is COLD, turn on fuel, pull on the choke fully, and kick the engine over. DO NOT use any throttle, when the engine is cold, and the choke is on. Remember Choke on, NO throttle.
When warm, no choke, and a little throttle when kicking.

You have the classic symptom of a dirty carb, has the bike been sitting ? What is happening is you are compensating for more fuel by activating the choke, you can try some "Techron" you get it at your local auto parts store its usually in the fuel injector cleaner area, this can sometimes dislodge and clean the jets, if that doesn't work then I would have the carburetor clean properly.