There are a lot of sites on the net with free plans that show you how to do this with lawn mower engines. But for the most part they are lower amperage output, and almost always 12-volts.
I thought about making one of these for camping / portable use till my brother bought a 2000-watt generator for $125.00. for that price it’s not worth the time to make one.
I’m sure it can be done on a larger scale with larger, higher output. But it may be more cost effective to buy a pre-made one for the higher output.
A 5000 watt inverter sells for several thousand dollars. So an inverter is not a practical part of a generator. You need to find some kind of motor or alternator that puts out your desired voltage & amperage.
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You can run, but you'll only die tired.