I think he's using the SloPro app, but I think it functions similarly to the stock app. Once you capture the slo motion video with the 5S, open it in the photos app. iOS 7 automatically positions starting and stopping points for slow motion/regular speed transition points. You can adjust these points in the photos app. AFAIK so far you can't add additional start/stop points but I haven't played with it that much yet.
Here's a little video I did of a ceiling fan I took at work to check out the slow motion feature. The blades look pretty clear in slo-mo.
Kadelic is correct about the SloPro app. I use it to capture slo mo clips instead of the stock camera because it allows me to apply the slo mo effect multiple times and also allows you to vary the slo mo speed. I've been using it since the 4s running iOS 5.x but it only did 60fps in 720p. The app also allows you to save the RAW clip to your camera roll.