Yes that old 5 ton is a lot, but when I was running everything last week, I had the oven on, at the same time as the clothes dryer. Every light in the house, garage and pole barn. All the low draw stuff that's always on, and the water heater kicked on for a bit. With everything running except the AC, I pulled close to 13kw (my gen says it will power 13.5 continuously and 15kw for one hour out of every 10). So I turned off the oven, and turned on the AC. It started, and I only hear a very momentary change in the sound of the engine as the AC licked on. everything still kept running as it should. After 15 minutes, I gradually reduced the loads until it was powering only about 2kw. Then switched back to utility, where the controller still keeps the gen running for a cool-down period (programmable). Mine is set to 3 minutes, then it shuts down.
My AC unit is 25 years old this year, and other than me replacing the start cap and putting in a hard start unit in about 5 years ago, it has never been serviced. Each year I plan on replacing it with something more efficient (it might be 10 SEER), but then it runs fine, and I let it go. If I keep it any longer, I'll put a HyperTherm Softstarter on it. When I do replace the system, I will plan on moving the soft-start over to the new unit, as I am sure they do not come with one installed. Either way, I think the gen should be fine handling a 5 ton