I have images taken in RAW on my Nikon D3400 and Photoshop CS 5.1 won't read them. I downloaded both the version of Adobe Camera RAW for Photoshop CS5 and the new updated version and also the DNG converter. It still won't open. When opening in Photoshop, it says the file is from a camera model not supported by Camera RAW.
From Adobe, the Nikon D3400 needs ACR (Adobe Camera RAW) v9.7 (or Lightroom CC / 6.7).
The last version of Camera Raw supported by CS5 is v6.7 (Camera Raw 6.7 Update is the last update of CS5 as you can see on the official Adobe Photoshop update page. It seems that some people copied with success files from ACR v7 (in Lightroom) into the CS5 installation (link) but I doubt you can do it with the v9.7.
In this new year 2017, some hope remains: What you can do is download a standalone version of ACR and convert your file into DNG format before opening them with Photoshop CS5. See here to get the converter.
If you want to keep the same workflow and directly work on your RAW, you need to buy the last version of Photoshop...
Short answer: it works if you install the latest version of adobe dng converter.
I've asked a friend with cs5 to open a dng file taken with your same camera as yours, D3400. Here is the print screen. You can see the acr version and camera model. http://i.imgur.com/vVaTaVR.jpg
The sample raw file was downloaded from http://www.photographyblog.com/reviews/nikon_d3400_review/sample_images/