Yes, OpenGL 4.3 was released August 6, 2012 and is supported on the Radeon HD 5000 series and newer.
Your card only supports OGL 3.2 out of the box. Driver updates should have brought it up to OGL 4.2.....
You would have to upgrade your OS to Windows7 or Windows 10 to get the later OGL extensions.
Thank you very much for your answers!