We are going on a 15 day National parks bus trip this year. Yellowstone, Arches, Mt Rushmore, Grand Canyon, etc. I shoot with a Nikon D5300 camera. I have a Nikon 18-55, and a 55-200. I am looking at adding the 200-500. In addition I like to take pictures of birds and wildlife. I would appreciate your thoughts.
If you need to get Nikon, then the 200-500 is a good bet. If you are open to getting something a little sharper, an extra 100mm of usable focal length* and with better dust and moisture sealing, configurable focus and stabilization parameters, has an Arca Swiss compatible lens foot, weighs quarter pound less and costs $100 less, then you might want to look at the Tamron 150-600 G2. I like it as much as my much heavier Sigma 150-600 Sport, which I also like as much as my Nikkor 600mmF4. The 200-500 isn't quite, in the same league, but I am being very critical, it is still a very good lens capable of taking great shots.
*by usable focal length I mean that it's not just a number - many lenses, including the 200-500, get a little soft at full zoom. Center performance on an MTF chart drops from a high of 2658 @ F5.6 at 300mm to 2143 @ F5.6 at 500mm - almost a 20% drop in center area sharpness. At 500mm and F8 it increases slightly to 2244.https://photographylife.com/reviews/nikon-200-500mm-f5-6e-vr
The Tamron does not - it is just as sharp at 600mm as it is at 500mm.
The reviewer in this article came to the same conclusion:https://photographylife.com/reviews/tamron-sp-150-600mm-f5-6-3-g2
I consider the Tamron to be every bit as sharp as the Sigma Sport, which in the 200-500 review provides an MTF figure of 2607 at F6.3 and high of 2711 at F8, both at 600mm. At it's best, beats the Nikon by 20%. I cannot put my finger on sharpness tests for the G2, but I did recently shoot with one and found no lack of sharpness at all, and I do recall reading that the sharpness was comparable and even a little sharper at shorter focal lengths.
Taking an 18-400 would leave me regretting not taking a better lens, and taking a bridge camera even more so. I shoot with a Sony RX10m4 which is about as good as it gets for a bridge, and though I am happy with the compromise of weight&size against image quality, they kind of trip you are taking would certainly warrant a better choice. Don't get me wrong - I love my Sony, but it is no Nikon D810 or even a D800, which is what I normally shoot with.