A 10-gauge cord at 75 feet is fine for that AC.
Yes. For a 15-amp portable air conditioner on a 75-foot run, a 10-gauge extension cord is more than adequate—and actually safer than going lighter.
Voltage drop is the real concern with long runs. At 75 feet on a 15-amp load, 10-gauge copper wire drops about 3.6% at 120V, which is well under the 5% threshold where equipment starts to complain. A 12-gauge cord at that same length would drop nearly 6%, so you’re right to step up.
Also, a 10-gauge cord is rated for 30 amps at shorter lengths, so it handles the startup surge from the AC compressor without breaking a sweat. Just make sure the cord is outdoor-rated (if needed), has a ground, and isn’t coiled up while running—coils trap heat.
You’re not overthinking this; you’re doing it right. Don’t let anyone tell you a 14-gauge “heavy duty” cord is enough at 75 feet. It’s not.