The Wattage rating numbers on generators can be confusing because many buyers/users do not understand "surge rating" as compared to constant load rating.
Consumers usually buy underpowered portable generators and are disappointed when it will not operate everything in their house or shop. Advertising of the generator products are questionable at best.
Manufacturers (especially the cheap ones) often boast their surge Wattage rating numbers in bold print while minimizing the steady Wattage rating. Wattage numbers are manipulated because the general public does not understand that Wattage is the work produced by the generator. The more work you want out of a generator, the higher the Wattage rating must be.
There are generator Wattage calculators online for reference of minimal generator requirements.
To clarify, surge ratings are meant to calculate sudden temporary loads such as a refrigerator/freezer compressor starting. Or a A/C compressor start up. Once these components startup they run on steady Wattage.
Sorry a 5500-Watt generator was not designed to run a whole house. They will get a person through a cold snap or summer power outage using a few lights, a refrigerator or microwave and a couple of small space heaters. They are not meant for running main A/C heat pump units. Even a window A/C unit puts a strain on them to a point that the generator can/will stall, or the window unit will fail due to repeated lack of startup Wattage. Under supplying the startup Wattage is a slow death for any electrical motor.
In reality, a "whole house" house generator rating starts out at the minimum range of 12,000 Watts (12KW).