Engine driven A/C is really you're only good option, unless you only want to use it when you can plug in an extension cord.
The problem with window A/C from your battery/alt/inverter: A 5000 BTU A/C unit is ~850 watts, which would be is 7 amps at 120v. That would require 60A at 14v, but the inverter is not 100% , so it would need more than 72A to run it through an inverter. You'll definitely want a pure sine inverter, as motors don't like modified sine, and will use even more current to operate.
72A is likely more than your alternator can put out at idle. If you have an electric fan, they draw 20-30A, so add that and you have a 90A load on the alternator... Even if you have a modern 120A alternator, that's a LOT of static load, and your alternator and batteries will not like it long term. Alternators only put out rated amperage when they're spinning pretty fast... At idle you'll probably only get 30% of rated output.
On top of that, starting current for the A/C unit is easily double or triple what the running current is, and it'll take a big inverter to start it. And big inverters need bigger batteries, since you can't just pull huge amps out of a small battery without tripping the inverter's low voltage alarm. I'd recommend a 2000W or bigger inverter, and two Group 27 batteries for the best performance. That would also cover times when you're idling and the alternator can't keep up too.
I'm not saying it can't be done, but it probably isn't the best plan long term. Especially since you'd have to hang the back of the A/C unit outside of the interior of the Jeep. I don't think there are RV style roof mount units as small as 5000 BTU, but if so, that would be ideal if you have a hard top. Or if you can find a 12v unit out of an ambulance or something like that, even better, since you could skip the inefficient inverter. I suppose you could go total hillbilly and knock out a rear window and plywood over it, with a window mounted A/C unit hanging out...
Depending on how your current A/C pump is mounted, you may be able to mount a second pump by just getting brackets from a different vehicle. It would be worth a little looking... YJ A/C parts are probably going to be difficult to find in a junkyard, but you don't know till you look... Retrofit kits are available, and they might even be able to supply a pump bracket that will work with your current setup.
FWIW, I had the A/C pump in my TJ converted to air compressor, but I fried it this spring by letting it run too long at high pressure. I'm planning to replace it, because I do like it, and it's all set up, but I have a Viair 400c pump mounted in my truck, and it's pretty fast too, particularly if I'm just airing up to 30psi or so. If I ever decide I want A/C, I'll not hesitate to go to a 12v compressor.
Sorry about the book... And Good Luck!