The RX100 III was first supported in Camera Raw 8.5 which is only compatible with CS6 and later.
So there is no Camera Raw plugin for CS5 which will open Raw files from that camera.
1. Upgrade to CS6
2. Join the Cloud
3. Free option: download the Adobe DNG Converter, convert all RX100 III Raw files to DNG format then edit the DNG files in CS5 Photoshop Help | Digital Negative (DNG)