Your 50mm lens
might be a macro lens. Some are. But many are not. Without more specific info about it, we really can't say. Is it a Nikkor? What, exactly, is written on it?
Some people define that as able to do 1:1 magnification, full "life size", or higher... Others folks, including some of the manufacturers themselves, define it as a lens able to do 1:2 magnification, or half life size. (Canon has a number of "Macro" lenses that are 1:2 capable.)
What 1:1 life size means is that with your D750 you can fill the image with a shot of something 24x36mm, the same size as your camera's sensor. For example, a US quarter (25 cent coin) is 25mm in diameter, so it can "fill" your D750's viewfinder at full 1:1. Your D5300 is an APS-C camera with a smaller sensor, so 1:1 with it means approx. 14x22mm area. I think a US dime (10 cent coin) is slightly larger than 14mm diameter.
Even if your 50mm lens is not a macro lens, it can be made to focus close and produce higher magnification by adding "macro extension rings" behind it. Those come in sets. Nikon makes them (but should be avoided because they're expensive and have limited capabilities). A set from Kenko in F-mount costs roughly $125 and included three tubes: 12mm, 20mm and 36mm. The more extension you put between the lens and the camera, the higher magnification it will be able to do.
However, you may not be happy with the image quality that produces. Simply, a normal or "non macro" 50mm lens isn't designed to focus super close. It's actually has some field curvature designed into it, probably optimized for 8 or 10 feet away. A true macro lens is a "flat field" design. This means is will be sharper from corner to corner, as well as more evenly illuminated. With a non-macro lens and extension tubes, it's not unusual to see some darkening of the corners of images, called "vignetting".
Now, these aren't necessary bad things. To photograph the yellow rose bud below I wanted a soft, dreamy look and chose to use a non-macro 50mm lens with extension tube specifically because I knew it would produce those effects. I also didn't need full 1:1 magnification. This is probably around 1:3 magnification, I would guess:
In my opinion, 50mm is somewhat short for a lot of purposes and the most versatile macro lenses are around 100mm. This is long enough to give you reasonable working distance for many subjects, without being so long that it's difficult to get a steady shot.
Shorter focal lengths get awfully close when focused to high magnifications, which can be a problem with shy live subjects and make it difficult to not shade your subject. Longer focal lengths are not only challenging to hold steady, more likely to require a tripod, but it's made worse because they tend to have extremely shallow depth of field, too... which can require you to stop them down more. Besides, it appears Nikon has quietly discontinued their 200mm f/4 Micro lens.
That still leaves you a lot of choices. Nikon themselves makes a 105mm f/2.8 "Micro" lens that's very good. There also are a Tamron 90mm, Tokina 100mm and Sigma 105mm.
The Tamron and Sigma would work fine on both your cameras, are very capable and cost less than the Nikkor 105mm. The Tokina is the least expensive of all, but it would only be able to autofocus on your D750. It will be manual focus only on a D5300.
If I were buying a macro lens today, I'd seriously consider the Sigma. It's a really nice lens, with all the features of and image quality competitive with the Nikkor 105mm. The Sigma actually used to be the most expensive lens around this focal length, but Sigma dropped the price considerably a couple years ago and it's now a very good value. The Tamron is also a fine, full featured lens that's the latest in a line of 90mm macro lenses they've offered since the 1980s.
https://www.bhphotovideo.com/c/products/SLR-Camera-Lenses/ci/274/N/4288584247?sort=PRICE_HIGH_TO_LOW&filters=fct_a_focus-type_5738%3Aautofocus%2Cfct_lens-mount_3442%3Anikon-f%2Cfct_lenses-kits_7315%3Alenses-only%2Cfct_special-designs_3320%3AmacroYour 50mm lens i might /i be a macro lens. Some ... (