Unless you plan to use a tripod, I'd recommend the 80-400mm (or the similar Tamron 100-400mm).

The 200-500mm is a nice lens, but it's pretty large and heavy... over 5 lb. and using 95mm filters.

The Nikkor 80-400mm is much more "hand holdable" at about 3.5 lb. It uses 77mm filters.

The Tamron 100-400mm is even lighter at about 2.5 lb (without tripod ring, that's sold separately and might add 1/2 lb.) It uses 67mm bilters

Of the three, the 80-400mm is a "pro-grade" lens and the priciest at over $2000.


Thanks much for the info and the photos. Because the lense I buy will be used mostly for daytime baseball and I never know how close or far away I can get, the flexibility of 80-400 will probably be what I end up with. Thanks again.
The 200-500mm is a relative "bargain" at under $1300. The Tamron is the most affordable at $700 (the tripod ring for it is an add'l $129).

All these lenses require pretty good light. They are f/5.6 or even f/6.3 at their max. focal lengths. Faster lenses are available (f/4 and f/2.8), but are extremely expensive, big and heavy.

Since we're sharing racing photos, I shot these with a Canon 300mm f/4 lens (<3 lb., 77mm filters, $1300)....



And that same 300mm lens with a 1.4X teleconverter added....



I do a lot of work now with a Canon 100-400mm (especially on APS-C cameras, for sports and wildlife). No racing photos with it yet. It's similar in size and weight to the Nikkor 80-400mm.

My kids play travel ball too and shoot with my d500 and 18-300mm or the 80-200mm. However, I stay close to the action either by using a step ladder and shooting over the fence by 1st or 3b, or just asking the umpire to shoot inside the field. This gives you greater flexibility. Umpires usually don't mind as long as you stay clear. Make sure to take your gear when you approach them so they know you are serious.

The only time I wanted a longer lens is when shooting behind the center field fence to home plate. I have yet to handle a 200-500mm lens, but the 18-300mm allows me to be mobile enough to shoot double plays and anywhere else the ball goes. But hey, if a long lens is in your crosshairs, by all means don't let me discourage you. I just wanted to share that using the smaller lens and a better shooting position you could probably do as well.

At my granddaughter’s soccer I can almost stand on the field so my 70-200 is fine. At baseball fields the best I’ve been able to do is near the outfield foul lines half way to the fence. I don’t want to take two lenses with me, so I’ll probably have to weigh flexibility of 80-400 vs. the reach of the 200-500. Thanks for the detailed response.
If you get the long lens, still try to get access to the field. Shooting closer to the grass gives you a great angle of the plays.

When I went to the FIELD OF DREAMS in Cooperstown Pennsylvania, I was privileged to have the opportunity to photograph my Grand Nephew pitching for his team. I prefer the Nikon 200-500 to the Nikon 80-400 for two reasons.
The 200-500 is a E lens, that means the aperture is electronic, meaning that when I am shooting 10 fps I know every exposure is going to be the SAME, not the same with the 80-400 which is not an E lens.
The second reason I like the 200-500 is because IMHO it is sharper throughout it's range especially at it's high end at 500.
Lets add a third reason, the 200-500 has more reach than the 80-400, on your D500 the 200-500 gives you a 750mm field of view compared to 600mm with the 80-400. And yes, this makes a real difference.
The image below is entitled, "Concentration", take a look at that tongue.