There are apps that let you grab a snapshot while shooting video, and in fact the iPhone 5 can do that right out of the box, no extra app required.
Of course, that assumes you can grab the still you want at exactly the right moment. It also assumes you're shooting video to begin with; most folks looking to snap a photo (like, say, a selfie) just snap a photo.
One solution that might provide better results: Vhoto, a free app that extracts still frames from iPhone video after the fact. And not thousands of individual frames you have to sift through yourself, but a culled assortment of the "best" pictures, as determined by Vhoto's proprietary tech.
That tech evaluates things like blur, contrast, faces, smiles, and, somehow, "user intent, to quickly extract the best moments from video. Vhoto's machine learning technology analyzes a user's choices and ensures that every time it processes a video, it gets smarter."
You can use Vhoto to capture video directly (using either the front or rear camera), though it can also work its video-to-photo magic on existing videos. (Alas, when you dive into your Camera Roll, you see both videos and photos -- which makes finding the former that much harder. The app should be smart enough to display only videos.)
Once Vhoto is done processing a video, it displays thumbnails of what it captured. Tap any of them for editing tools: Instagram-style filters, image adjustments like contrast and saturation, and flip/rotate. When you're done, you can download the photo to your Camera Roll or share it via the usual methods (Facebook, Instagram, email, etc.).
I did some quick tests with Vhoto, using both old and newly captured recordings, and the results were quite impressive. You really can find some hidden still-frame treasures inside a video, to the point where you might find yourself shooting a lot more of it.
After all, you're much more likely to get a good shot out of, say, a minute of footage than you are a millisecond. That said, Vhoto necessarily produces lower-resolution photos: 1,280x720, good enough for sharing and posting, but not ideal for printing.
Although it's compatible with all iPhones, iPads, and iPod Touches running iOS 7, Vhoto is optimized for iPhone 5. I think it's definitely worth a try, especially considering the price.