Just to confirm, make sure you have opened Lightroom CC 2015 not Lightroom 5 (previous version).
You will find HDR option in : Photo > Photo Merge > HDR
If you find HDR option, please select mulitple images to access this feature.
If not, click on Help > System Info
Please confirm the Lightroom version.
Just to expand on Mrinmay's reponse...
If you upgraded to LR CC from LR 5, the upgrade is a side-by-side install so that you have both versions installed. Often times the desktop icons do not get updated, so make sure you are running the newer version.
You need at least two photos selected. Then go to the Photo menu.
This is what is at the beginning of the system information text:
Lightroom version: CC 2015.1.1 [ 1032027 ]
License: Expired Trial
Operating system: Windows 7 Business Edition
Version: 6.1 
Application architecture: x64
System architecture: x64
This seems like the correct version. A few others have mentioned that I need to select more than one picture. I have done that and don't see the menu item.
Can you even use the Develop module, anymore? The screenshot says your trial of LR CC has expired, so only viewing and exporting of images is possible, now, I’d think.
No I cannot use the Develop module now. From the demo, it looked like it didn't need it. I'll see if I can get another trial from Adobe to see if the feature gets enabled.
I just bought a subscription. After the process was completed, the HDR feature appeared. Now I need to decide within 14 days whether or not to keep it or get a refund. I'll probably keep it as it's pretty good at what it does.
I am sorry for the inconvenience.
I would request you to provide the information as it will be very helpful for us to help you out.
Also, you may check your downloads folder for the image which you have downloaded.