It's not the same. The iPhone 5 can take many pictures in rapid suggestion on iOS 7, but it's not the same as the burst mode feature for the iPhone 5S. With the iPhone 5S, the phone will select the best of all of these photos, and show you that one. If you select it, you will get the option to view the others as well.
With the 5, they all show in your camera roll, there is no intelligent feature that automatically examines the photos and selects the best.
I know there are some other differences as well, but that's the major one.
So in short - the iPhone 5 gets "burst mode lite," the feature is only fully realized on the 5S.