Longer range means what to you? Tubes might give a bit closer focus distance, but definitely Not longer distance (the opposite). Whereas teleconverters give greater focal length for more range.
But extension tubes have less effect on longer lenses.
50mm is a lot of extension tube, and on say a 50 mm lens, it effectively doubles its focal length, and the combination should reach 1:1 macro (which is generally how the tubes are used). But 50 mm on 200mm is 25% increase, and on 500 mm is only 10% increase (not double), and will only have minor effect. Use with 20mm would be much more common than use on 200mm.
It is not sounding right. If you only want to focus at a closer distance (which is what tubes do), then compared to sticking with a 200-500mm lens, I'd suggest a shorter lens instead of the tubes.
If you want a lens longer than 500mm, then that's what teleconverters do.
Here is a list of Nikon teleconverter compatibility.
https://www.nikonusa.com/Assets/Common-Assets/Images/Teleconverter-Compatibility/EN_Comp_chart.html
The 200-500 is Not on that compatibility list. There are TC of other brands that might work.