It is all dependent upon how well the in-camera version is implemented versus how skilled the person doing the post-processing version is, as well as the capabilities of the post-processing tool that person is using.
It's certainly possible that the in-camera version Nikon has put into the D5600 can produce a result you like better than what you can produce by doing the post-processing of bracketed images yourself, especially if you have very little experience doing raw post-processing, much less HDR post-processing. Even when dealing with a single exposure, doing your own raw development allows you to show details from an expanded scene dynamic range than what in-camera JPEG engines will show.
In a sense, doing your own raw conversion from single exposures can also be a form of High Dynamic Range Imaging, a term which has been around much longer than digital photography has existed, and even longer than the more recent practice of producing an 8-bit tone-mapped version of a 32-bit floating point light map created by combining multiple bracketed exposures which came to be referred to as HDR.
It's also quite possible that your skill, either now or in the future as you continue to gain experience and increase your knowledge, can produce final results that you like better than what the camera produces using the automated routines. Don't be afraid to explore the possibilities! Don't let your less than earth-shattering initial results discourage you, either.
For those who are highly skilled doing it, there's no contest. Controlling every aspect of the workflow from image capture to final result allows the photographer to get as close as possible to what the photographer wants for a specific scene. That's going to be far better than what the engineers who programmed the camera guessed every photographer might want from every conceivable scene. Not only is this true for HDR photography using multiple exposures, but it is also true for doing raw development for each photograph or shooting scenario instead of letting the camera's JPEG engine reflect the guesses of those who created it.
It is true that as computational photography continues to advance with increased processing and larger memory capabilities of cameras, the gap between automated camera routines and manual post-processing is narrowing, especially for those not highly skilled in the art of post-processing. But a highly skilled person can still usually do "better", whatever that means when talking about making artistic choices, than even the best automated routines.
Perhaps in the future things will advance to a point where a highly skilled photographer can "teach" a camera or post-processing routine to automatically produce results that match their artistic intent for a particular type of scene? But we're not anywhere near that yet. We are already well beyond the point where automated routines can exceed the results from those with little or no post-processing skill.