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A 5500 watt genset will probably not push a 2-ton A/C unit. Even if it does, it would be pushing it to the limit. An hour a day would be pushing it.
Even if your genset will push it, your proposal to connect it to your home is both illegal and highly dangerous. It is a fire waiting to happen.
The ONLY way to connect a genset to a home is through an approved safety device, such as a transfer switch or a generator interlock device.