you download the catalyst software suite for you operating system and your line of radeon HD graphics in this case its the HD 5xxx series. install catalyst suite and IT will take care of the rest. the program will detect your card and any extra drivers it might need (like HDMI sound, open gl, open cl drivers and stuff like) and download the specific drivers for your card that are needed. it should be sort of straight forward.
this video should help
http://www.youtube.com/watch?v=FlxIvc16vQg