Can I take a photograph in Nikon D5100 with digital zoom?

Can I take a photograph in Nikon D5100 with digital zoom?

If I understand you correctly, no, you can't. I'm guessing you mean the zoom like feature on some bridge cameras?
Zoom on a D5100 is limited to the lens you're using.

No. Like all dslr's you use the optical zoom of the attached lens to zoom in on your subject. What might be confusing, is how you can digitally zoom in when you review captured shots afterwards. Digital zoom is a great way to degrade your images. Only use it when optical zoom isn't an option, or, on your computer, when you need to crop.