1) You could try to find out if your version on ACR supports that camera/s raw format or not (obsolete versions of ACR do not get updated for new cameras). Maybe post on the Camera Raw Forum or search Adobe’s website.
2) You could try using the free DNG Converter to convert the RAW files into DNGs which ACR 6/Photoshop CS5 should be able to handle.
The D5200 was first supported in Camera Raw 7.3
Camera Raw 7.3 is compatible with PS CS6 and higher. CS5 is not compatible.
1) Upgrade to CS6
2) join the Cloud
3) Convert all your Raw files to DNGs with the free DNG converter from Adobe