I have taken several photos on my iPhone 5 at 300 dpi. However, when I import these images into photoshop, they convert into 72 dpi images. I there a way I can fix this? The images are even saved at that smaller size.
If the image file contains a resolution value, then Photoshop will honor that value.
If the file does not contain a resolution value, then Photoshop will assign the default 72 pixels per inch.
It sounds like your photos do not contain a resolution value in any of their metadata.
The image does not get "smaller", and all the pixels are there, but the resolution value changes how the pixels are mapped into real world (physical) measurements.