No, it's not possible. Mk III files require PS CS6 with ACR 7.1 or LR4.
You could convert them to DNG using DNG converter 7.1.
Excuse me, but Camera Raw 6.7 handles Canon 5D Mark III files directly, and it works with Photoshop CS5, so Mylenium's answer is incorrect.
You just need to update your Photoshop CS5 installation to include Camera Raw 6.7. You may be able to do that by simply going through Help - Updates.
You can check your facts starting here: http://forums.adobe.com/thread/311515
Which leads you here: http://helpx.adobe.com/creative-suite/kb/camera-raw-plug-supported-cameras.html
Note specifically the "What version of Camera Raw started to support my camera?" section, which states: