When discussing if a particular camera's output is good enough, there are several considerations.
- Print size. The larger the print, the further the pixels produced by the camera are spread out. In the case of the iPhone 5, a 16x20 print figures out to about 150 ppi, which is about half of the normally accepted standard. On the other hand, the normally accepted standard applies to an 8x10, half the size of your 16x20. So an 8x10 printed at 300ppi has the same number of total pixels as a 16x20 printed at 150ppi.
- Viewing distance. The closer a print is viewed, the more critical the resolution of the image is. Standard viewing distance is about 10 inches/25cm for an 8x10. If the planned viewing distance of a 16x20 is twice that, you can get away with half the resolution. But if you want to be able to view the larger photo at closer distances, then the reduced pixel oitch will become aparent. Also involved in the equation is the visual acuity of the viewer. The 300dpi 8x10 @ 10" assumes a viewer with 20/20 vision. Some guidelines assume a viewer with 20/15 or better vision.
- The amount of noise in the original image. If a scene is well lit and allows an exposure where plenty of light strikes the image sensor of the camera it allows the Signal to Noise Ratio to be higher than an image made in dim light. Since variable light is the Signal and the Noise generated by the camera is fairly constant, a dim scene results in more overall noise in the image. With a camera such as your iPhone 5, the smaller pixels required to squeeze so many megapixels onto so small a sensor gives it a disadvantage compared to dedicated cameras with larger sensors when asked to gather as much light as possible in darker settings.
- The planned usage of the photo. If the print is for a critically judged competition or art exhibit, the iPhone 5 is probably not good enough. Even large prints will be viewed critically at close distances. If, on the other hand, the print will be a gift to the grandmother of child(ren) in the photo, it will probably be much more appreciated.