Nikon D5100 HDR is not available..

Problem:  HDR - This option is not available at the current setting or in the camera's current state.

HDR is unavailable (cannot be used) if Auto-Bracketing is on.
HDR is unavailable (cannot be used) if Image Quality is set to any of the RAW settings.
HRD is only available in one of the PSAM modes (you cannot be in fully-automatic or scene modes).

Issue:
With the Nikon D5100, HDR is not selectable if the camera has Auto Bracketing turned on or any variant of RAW is selected in the Shooting Menu, 'Image Quality.'  It almost goes without saying, the camera must also be in one of the PSAM modes, and not in the Green-Automatic mode.

This article is an excerpt from a longer, more detailed article:  Nikon D5100 Auto Bracketing


Solution:
Turn off Auto-Bracketing and/or
Turn off RAW

A.  Press "i" to activate the Information Display.

B.  Press "i" a second time to position the cursor along the right side.

C.  Arrow-key down to the BKT section (illustrated in yellow, above).
Click OK to select the bracketing option - e.g. "stops" -- set the value to "Off" to disable.

3. Choose "Off" to turn off the feature. 
(Note: Use this screen to turn off Auto Bracketing in mid-series)
 
4.  Turn off RAW.

Additionally, confirm the camera's Image Quality is set to JPG (FINE).  RAW, or any variant of RAW+JPG cannot be used.  See "i" menu, Qual, or Menu, Shooting Menu, Image Quality.


Additional Comments:
Rather than using HDR in-camera, consider manually using bracketed exposures and HDRing in software, such as PaintShop Pro, Photoshop, or Photomatix.  This way, you are not restricted with JPG-only.

Related articles:
Nikon D5100 Auto Bracketing - Full Details on the feature, including additional methods
White Balancing - Color Balancing
Using an 18% Grey Card - For better exposures