My experience with Nikon bodies is that they will recognise and work with any lens with the Nikon F mount, but only upper ranges such as D7*** series will you have full control and have exposure/f stops/metering as with such cameras you can program each lens as a "Non CPU" each its own focal length and maximum aperture, though having said, I've only used (very) old fixed focal lenses with this system.
Whether the lens would work reliably enough in the field on your D5200 though is another matter and therefore it may be better to buy/use a more modern lens where such problems won't arise. A working AF is really a must for this type of lens too and as you say, it won't operate on the D5200 (but would on D7*** as they have inbuilt AF motor)
Try the combination if you can before you buy but I still wouldn't really recommend it and it's also a very old Sigma lens, when Sigma didn't make good lenses!
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