What EXACT version of Lightroom?
What model of Nikon took the image?
How would the images downloaded?
Did you use Nikon Transfer to download?
If you have a subscription to the Photographers plan then you should be running LR Classic CC V7.1 and not LR 2015.
What operating system is installed on your computer?
What camera are you using, Make and Model number?
In LR please go to the Help menu and select System Info and post the first 4-5 lines from that.
I'm using Adobe CC 2015.5.1
A Nikon D3400 took the images. (It's brand new)
I don't understand what you mean by how they would be downloaded, but they're on an SD card and I am attempting to open them directly from the SD into lightroom
I synced my phone up to the nikon Snapbridge app which sends the photos directly to my phone but because I don't have great storage on my iphone I disabled this feature whilst taking my snaps, and did notice that the pictures in lightroom that didn't get sent to my phone don't seem to show a preview on the import page
What operating system are you using? Windows or Mac OS X. If OS X what is the exact version number, 10.?.?.
How are you getting the images from the memory card to your computer?
Are you using a Card reader or are you connecting the camera directly to the computer with a cable?
Ive been using this version of lightroom for about a year now and everything has been fine until I took pictures with my new nikon d3400, I have the full adobe package with photoshop and everything else included.
operating System - Apple Macbook OS X Yosemite version 10.10.5
camera - Nikon D3400
Lightroom version: CC 2015.5.1 [ 1073342 ]
License: Creative Cloud
Operating system: Mac OS 10
Version: 10.10 
I see you are using a Mac. Please state the version of OS X that is running on your Mac.
Also it seems you have chosen the Add option in the Import dialog window of LR. If you are connecting the camera directly to the computer you can't use that option even though it might be available, Selectable, in the import dialog.
You need to use the Copy option to Copy the image files from the card to a folder on your Mac's hard drive.
You need Lightroom CC2015.7 or higher to open files from the D3400 and you are using CC2015.5.1. Update Lightroom (the last free update version for your license is CC2015.14.
Ok the reason you can't update to the newest version of LR is because you are running an older version of OS X. But you can update LR to 2015.6.1. You can do that from the link below.
As stated above you need a version of LR that won't run on the version of OS X that is installed on your Mac.
The highest version of LR you can run on OS X 10.10.5 is LR 2015.6.1 and you need at least LR 2015.7.
So you have 2 options.
1) Use the Free Adobe DNG converter program to convert the NEF files into DNG files and then they will import into LR.
2) Upgrade OS X to the new version, High Sierra 10.13.2. But if you do that you might have some older software that might not run on the newer version of OS X.
Ok this is all starting to make sense now,
I don't really have any particular software that would be affected by an operating system upgrade so I may give that a shot.
Once i've done that i'll upgrade my version of lightroom.
I'll report back
PLEASE, PLEASE Do a Complete system backup before you do the OS X upgrade.
Apple and OS X and Mac's aren't perfect. Anything can happen when upgrading the operating system.
Without a current backup if the upgrade fails or gets stuck you will lose all your files, work.
duly noted and thanks
Thanks for all your help
You are welcome.
I'm having this same problem - unable to open raw files. I'm using a new Nikon D850.
Lightroom version: 6.4 [ 1060496 ]
Operating system: Windows 10
You are correct! I had to re-download Lightroom 6.0 and then add the patch upgrade 6.14. I'm good to go now. Thank you.