But, according to the developers, the recommended graphics card is an ATI Radeon HD 5870.
Provided that you have at least an ATI Radeon HD 5770 graphics card you can play the game. If possible, make sure you have 4 GB of RAM in order to run Crysis 3 to its full potential.
Crysis 3 system requirements state that you will need at least 3 GB of RAM.