Nikon D600 was fully supported when Adobe Camera Raw 7.3 launch however there was preliminary support for Nikon D600 in Camera Raw 7.2 and
Photoshop CS5 does support Adobe Camera raw files from 6.0 to 6.7 only.
For more information please check.
Camera Raw plug-in | Supported cameras
Camera Raw-compatible Adobe applications
If you don't plan to upgrade from CS5 anytime soon then you can convert the Raw D600 files to DNG using the free DNG converter.
Then edit the DNGs in CS5.