Can you use a Sigma 50mm 1.4 ART or any Sigma ART series lens on a Nikon D5100?
Will it be able to autofocus?
Is is only for full frame Nikon bodies?
Yes, if you buy it in Nikon mount.
It will autofocus (HSM is Sigma's equivalent of AF-S, meaning that the lens contains a focus motor).
On Nikon, the last is irrelevant (any cropped-sensor DSLR body takes the manufacturer's full-frame lenses, it's only Canon who have problems the other way around). What is a standard lens on full-frame becomes a short portrait lens on your D5100.
Personally, I think it's a lot of cash to lash out on a lens that does little a 50mm f1.8 AF-S Nikkor can't do as well (do you Really need the extra half stop?), but that's your decision.
It will work on the D5100. As Andrew points out, it is a lot of money whose value would not be very noticeable on the D5100. On a full frame camera, especially a high resolution one, it may justify its expense better by being sharper at the corners of the full frame than less expensive lenses that show their limitations on the full frame. The DX sensor tends to crop out the part of the image circle where the difference tends to show.
On taking another look at the review of the Sigma ART lens
http://www.cameralabs.com/reviews/Sigma_50mm_f1-4_DG_HSM_Art/
it seems that even in the center it can offer some superior sharpness at full aperture compared to less expensive lenses.
Of course in deciding to invest in such an expensive 50mm prime, you should spend some time with your kit lens set on 50mm to decide if you are going to use this focal length often enough for the bump in quality to be worthwhile.
If 30mm is a more frequently useful focal length, the Sigma 30mm f/1.4 DC HSM Art Lens for Nikon is a smarter buy is you want to step up to the quality of a prime lens.
As a portrait lens, I don't buy the current craze for 50mm on a DX camera. That is the 35 equivalent of 75mm, and back in the 135 film days there was no 75mm portrait lens. 85mm or 105mm were typically used for that. A 60mm macro would be the 135 equivalent of 90mm. Right for portrait, and also giving good service for macro.
As long as it fits, yes. The Nikon can do art too, you know.