I'm really trying to find the best all around setup. For family vacations we hit up a different National Park every year, so the ability to reach out for critter pictures is a must. I also need to be able to take the occasional landscape photo or picture of the kids.
I carried the 5600 on an elk hunt 2 years ago and it just became too cumbersome and heavy and ended up getting left at camp after the second day.
A mirrored camera will do everything a mirrorless camera will, with the exception of a mirrored camera being slower. This can make a huge difference in action shots, where the mirrorless cameras have a huge advantage. If you are looking for smaller and lighter, there are other fixed lense, lots of zoom options available.
Honestly, you should be talking to Doug, or Joel. Joel replied above.
The reality is the camera you have is a very good camera in its class. Nikon has said that they will be phasing out the 3000 and 5000 series cameras. To invest any money into a mount that they are showing they will not be supporting for the long haul is not something I would suggest. They, like every other company are moving to mirrorless. They are late to the party but they will get there. Before investing any more money into the F mount look at the Canon, Sony and Olympus crop sensor cameras. Call me to discuss your usage and what would be the best for that. I am here today until 4:30, Saturday from 9-5:30
The advantage of a mirror is the optical viewfinder. The age old Nikon F bayonet mount on your D5600 means you can use the plethora of already manufactured lenses that are in the world. So you theoretically can get great glass at a fraction of the price of the latest and greatest. However, mirrorless cameras are quieter (no mirorr flipping up and down), smaller and the current paradigm.
On your 1.5x crop sensor Nikon you are getting an effective 900mm lens on that 150-600. If you need that reach, be sure to get a similar crop factor mirrorless camera. And factor in the cost of a new lens with the reach you need. Things can add up.
The OP has probably made his choice. For me, I decided to put off Nikon F mount lense purchases. F mount lenses can use an adapter and fit on the Nikon Z mount. But, you don't get the advantages of the Z mount and the Z mount lenses, even in comparable price points are better.
I think in 10 years DSLRs will be about as common as 35mm film was in 2010. I think the result will be a loss of value in lenses designed for 35mm/DSLR mounts. So, the 2k lenses I want can wait as I don't intend on replacing them for 20-30 years, but technology changes make upgrading bodies worth while.
I've got upward of $10K invested in DSLR Camera and compatible lenses. They seem to work just fine for the stuff I do. Chances are I will not be switching to Mirrorless across the board. I could see buying a mirrorless body and something like a 24-70 f2.8 lens.