I purchased Nikon D5600 last month.
While doing bird photography I realize, 70-300 mm lens is not sufficient. I have few queries:
(1) Which lens is recommended for wildlife photography? I checked for 150-600mm, but did not find in local market for Nikon. Mostly Canon compatible lenses are available.
(2) Is D5600 suitable for such photography or shall I upgrade to D7500 ?
Focal length does not much depend on the bird or the camera, but instead depends on the distance to the bird. Is distance 3 meters or 30 meters? The camera you own is likely very fine. Use it to learn if your use actually needs any other feature.
I have taken some very beautiful bird pictures with a 55-250mm lens on a crop sensor entry-level Canon DSLR. It's 400mm equivalent (35mm). On your Nikon, the 300mm is 450mm equivalent (35mm), i.e. longer.
I would say a much longer lens would be significantly harder to aim. But, since you have a crop sensor camera, a lens zooming to 400mm, 500mm or even 600mm would be an option. These are 600mm, 750mm and 900mm equivalent (35mm), i.e. very long. Unfortunately, they cost more than a 70-300, and the weight is something totally different than the weight of a 70-300. They also are physically longer.
On the other hand, I don't always get many keepers with a 400mm equivalent (35mm) lens. I think these factors affect the number of keepers:
...but perhaps the largest factor is just the amount of luck.
I have given up trying to photograph small birds in flight because they fly so quickly and on such an erratic path that it's almost impossible to get keepers.
Remember to use continuous focus, and set the shutter speed to 1/1000 to get good pictures that are in focus and don't have motion blur, if photographing during the daylight. In anything other than daylight, things become significantly harder.
I also shoot a D5600. You might take a look at Sigma lenses. I invested semi-heavily in their EX series of pro lenses (pre Art & Sport), purchasing them as refurbs from the Sigma Outlet to save a few bucks. Several of their DG lenses (full frame) work very well with crop sensor bodies, to the point that hood extenders are provided for crop sensor. I have an APO 70-200 2.8 that I can use Sigma APO teleconverters on to add reach. That makes the 200 become 600, effective length after crop factor with the 2x TC. All are currently discontinued, but the lens is available as noted above and the TCs can be had on the used market. The combination of huge lens on a small DSLR looks a tad odd, but it really takes nice photos.
Birds are small and far away. I use a Nikon P900 with a 2000mm effective lens. I can find the bird in that small a field of view, sometimes using the zoom out feature on the camera but not always. I see people with DSLR cameras and 600mm effective getting pictures comparable to what I get because the larger sensor pixels let them crop tighter. On one of my walks somebody had a Nikon DSLR with a 500 mm prime and a 1.4 extender on an APS-C sensor that gave 1120mm effective with much larger pixels than I have, so should be much lower noise. It would have been nice to put our pictures next to each other. I think he would have won where the birds filled the frame and I would win when we crop hard, but I don't have real evidence. I could harp on the fact that I was carrying a lot less weight, a lot less cost, and had a zoom so if the bird was close I could deal with it, but I don't feel that answers the question-what is the best rig to get the best photo here? Depending on the birds you are interested in, manual focus is important. Many birds are behind obscuring brush. My P900 claims to have manual focus, but it doesn't work. If you have a real focus ring you will get those photos if the bird sits still long enough to focus manually. I also have a Canon 7D with a 100-400 mm zoom and APS-C sensor. When I go looking for bird photos I carry the P900, which gets some more than the Canon and misses some the Canon would get.
It is hard. Keep trying. You will learn what works for you, which may come from what equipment you start with.
Sigma has nikon compatible lenses-- I'm looking at getting one myself. They have some lenses that go to 600mm
