5,000btu AC unit will not run o 1,500 watt inverter. Why?

You first said #12 wire (very small) and above say #2 but that would not have fine wires so I think you missed the 1 and it's really #12. That's too small.
Check the voltage at the battery with a multi-meter at the moment the A/C tries to engage. I suspect it drops to less than 12V or you will find the tiny wires getting very warm trying to get that much juice through those wires.

Two issues
Only one battery, doesn't matter that the T/V was running, the feed wires from there to TT battery are too small to carry the surge current needed, that battery is trying to do it all
If you want to try again, connect another battery

Second is possibly the response time of the inverter
Ok it's 3000 Max, but how fast can it get there from zero output to the compressor lock rotor amps to start the compressor running, and how long can it sustain it using one battery

Been on the road all day. This was just a test to see if it would work with this inverter. The TV was running and the voltage reported by the inverter was 14.2 volts. I had the inverter connected directly to the TV battery with the supplied 18 inch cables that came with the inverted. I would say they are maybe 2 gauge fine strand copper cables.

There was no error reported. The AC would try to start, but the compressor would freeze and just make a knocking noise. Since the unit is rated at only 515 watts and the inverter has a peak rating of 3000 watts, I find it hard to believe that the AC unit would have that steep of a start up curve.

Nothing else was running in the TT or the TV, so all power was available to the inverter and the AC. My best guess is that this AC unit cannot work on a modified sine wave. I have seen this configuration work in the past on small ac units, and it is quite common on boats. But if I were to set it up as a serious endevour, I would add a deep cycle to the TV and upgrade the TV alternator to a much higher amperage or install an additional alternator just for inverter.

I was running 15K AC on inverter/charger rated at 2600W, but that was high end Xantek
In my application the conversion huge alternator would provide 24V and 4 GC batteries would be only equalizer.
I gave it short try one time and AC would run about 20 minutes on 4 batteries.

time2roll wrote:
I figure the tow vehicle start battery should start and run it for at least a minute.

Yep, and it will love seeing 10 volts. LOL Keep doing it over and over and see how long it lasts.

I figure the tow vehicle start battery should start and run it for at least a minute.

I'm sure it's a MSW inverter (not good) and we don't know the battery cable ga and length, and what type of battery or its SOC.

Access GOOGLE

Search CAPACITOR TYPE ELECTRIC MOTOR START AMPERES

And then....

Connect a voltmeter to your batteries start AC What do you see.

If it had started, how long do you think it will run on one battery before getting to 50%?

What is your battery(s) capacity?
Was anything else running at the time?
Plus all the questions from above.

Need more info......