LR 4.3 or higher will open D5200 NEFs if nothing is wrong with them. Since LR 5 is having problems, the files are likely corrupted.
The most common problem is that older Nikon software Transfer/ViewNX was used to work with these newer files and the obsolete software has changed something in the files that makes them unrecognizable to Adobe products.
First test with an NEF that you copy directly from the memory card to the hard-drive of your computer without using or touching it with any Nikon products. If this works then you’ve likely found the source of the problem, and either install Nikon products that are at least as new as your camera or stop using Nikon products with raws from your newer camera.
The corruption to already corrupted files can be reversed using a utility from here:
http://owl.phy.queensu.ca/~phil/exiftool/fix_corrupted_nef.html