Hi, best thing to do is just work it out yourself to put your mind at ease.
Run gpu-z and log it while playing the game. Then look to see if your ram speed increases when the game is running, best make sure it is in full screen mode. If it does, then you will know the card is running properly as the bandwidth is calculated by the frequency of the ram multiplied by the bit width which I believe would be 256 for the 5870.
Also note that due to the use of gddr5 you will have to multiply the frequency by 4 for the effective clock speed.
This should help make sure everything is working fine.