Probably the reason iPhone 5s doesn't have OIS

Here's probably why the iPhone 5s doesn't have optical image stabilisation at the hardware level, like the LG G2:

It (iPhone 5s) takes multiple images and then uses the best bits of each picture based on exposure and sharpness to composite together a final image. (for every single still shot)

Theoretically, we’re looking at something that could replace a blurry face, for instance, with a sharp one from just a second later. Typically, shooting a sharp picture in really low light requires two things: a steady hand and a steady subject. Stabilizing only the lens( which is what hardware-level optical image stabilisation does) solves only one of those problems. It doesn’t matter how steady your lens is if your subject is fidgety.

Although we don't know how Apple's auto image stabilisation works in real life, it seems like Apple may have a better( or a more complete) solution to reducing blurriness in stills. All thanks to the tight integration between the software and the A7 chip(more specifically, the ISP in A7) :)

quote cited from techcrunch