There are several apps available for low-light and light trail photography. Slow Shutter! (on sale for US$0.99) is a fine example, and has been rewritten to make it easier to use and increase performance. The app has replaced complex settings with Auto mode (waterfalls, moving objects), a Light Trail mode (traffic, fireworks, moving lights) and a Night Mode for shooting in dark places.
The app supports shooting at full resolution, and you can adjust exposure when you are not in auto mode.
I gave the app a try and found it worked well. Moving water in auto mode looked quite good. Focus was pretty fast, but the darker the environment the longer a focus lock can take. About the only area where the app didn't excel was at night mode. I thought the basic iPhone camera on my 5s did very well in low light, and I didn't see much difference in noise. Both setups will make you want to have something to steady the camera against, or use something like a Gorilla Pod.
To test the Light Trail mode I shot an LED clock and moved the camera during exposure. Then I tapped the camera icon again to stop the shot. The results were nice, with low noise and a sharp image.
For light trails and the auto mode, Slow Shutter! was excellent, and could not have been easier to use. Saved photos go right to your camera roll, or you can mail an image or message it to someone directly from the app.
Slow Shutter requires iOS 7 or later. It's a universal app and it is optimized for the iPhone 5.