For what those things cost, you can bet they last much longer than 800 hours when taken care of properly. They are king of the hill for a reason.
Running a 5000 BTU air conditioner is easy, starting it depends on the unit, temperature, altitude and the surge ability of the generator. I spent a year finding out which unit used the least so my solar could run it. Starting it requires a battery to give the umph the compressor needs to get going. Getting it going again when the pressure has built up is even harder so you may have to run it full blast so that the compressor doesn't cycle. There is a you tube of someone doing this.
https://www.youtube.com/watch?v=QnsCfRsrevg
