The average central A/C will use 4000 to 5000 watts. I own the cheapest smallest window unit at the store and I just checked it's about 600W (4.8 amps @ 120V).
It's not horrible, but that's like half a space heater and most people spring for something bigger.
Peak draw. Duty cycle is about 1/3 that typically.
First hour use may approach peak, but again, most of that is incurred regardless.
5 kWh is $0.50 - $1.00, which is the cost of running an hour long for a day, the worst-case scenario. You'd spend a lot more on IoT kit (the Turris Omnia alone is $300) for minimising that cost.
It's not horrible, but that's like half a space heater and most people spring for something bigger.