You are correct that LR 5.3 should support this camera. But you do not "open" in Lightroom. You need to import them. Is that what you are doing?
I can't speak on Elements.
What exactly do you mean, please describe in detail, "cannot open any raw files". What steps are you trying in Lightroom, and what happens when you try those steps in Lightroom, and what is the error message.
Did you use any Nikon software at any time in the handling of these photos, before you try to open them in Photoshop Elements, or import them into Lightroom?