Are you using PREMIERE Elements or PHOTOSHOP Elements?
http://forums.adobe.com/community/photoshop_elements if Photoshop Elements
Otherwise, what are you trying to do when you "apply setting then click save" with that picture file in a video editing program?
Welcome to the forum.
Along with John T's question (if you are using Photoshop Elements 12, then a MOD can Move your post to that forum), I would assure that you have the latest version of Adobe Camera RAW (ACR) plug-in, and also check that it includes support for your new Nikon. Camera mfgrs. add new Camera RAW specs, with new models, and sometimes, it takes Adobe an update, or two, to get those new specs. into the ACR. Each version of ACR will have a list of supported cameras. I know that one new Nikon was not in the last ACR update, but forget the exact model. That one WILL be in the next version of ACR, but that might not be available for a few weeks.
Good luck, and let us know the exact program that you are using, please.
Photoshop Elements 12 is up to Camera Raw 8.1, with an Update to 8.2 after updating. And, your Nikon 5100 camera was supported starting with Camera Raw 6.4. So that does not seem to be the core of the issue.
The above is supported by the fact that you can open the Camera Raw dialog, can edit there, but, when you go to Save the edit, you error out. By the way, what version of Camera Raw is shown on the dialog that is opening and in which you are editing your raw image?
Is the problem only with the "Save Image" option in the Camera Raw dialog? Or, does the error come later when you are in the Save Options dialog that should appear after you hit "Save Image"? Do you get an error message if you click "Done" or "Open Image".
What do your computer resources look like?
From what you wrote, your problem is a Photoshop Elements 12 one, not a Premiere Elements 12 one. One never sees the Camera Raw dialog in Premiere Elements, only Photoshop Elements.
Do you have Premiere Elements 12? If so, can you import your raw image into it with its Add Media/Files and Folders? Camera Raw dialog is a feature ONLY for Photoshop Elements. But in your situation the install of the Camera Raw plug-in will allow for the import of a raw or dng image into the video editor Premiere Elements.
I would encourage posting this question in the Adobe Photoshop Elements Forum.
Looking forward to your results wherever it is placed.