I think you'l find that its 72 PPI ie pixels per inch. The PPI setting only matters when you come to print your image. 72 PPI is way to low to produce acceptable prints. For home printing, using my Epson 1290, I usually aim for a minimum of 150 PPI as a minimum, and preferably over 200. The figure of 300 PPI that you mention is the recognised resolution usually required by commercial printers for magazines.
Changing the PPI affects the output size of your image when printed, but does not change the actual file size. So for example your 5184 x 3456 image printed at 72 PPI would produce a print 72" x 48"
(5184/72 x 3456/72). Printing the same image at 300 PPI would produce a print 17" x 11.5"
To change the PPI in PS go to Image > Image Size, UNCHECK Resample image and enter the desired PPI eg 300 in the resolution box - the document size will change but the number of pixels in the image won't.
DPI = dot per inch and refers to the nunber of dot of ink a dot matrix printer puts onto one inch of paper. For example my Espon can print at 2440 DPI.
DPI & PPI are completely independent (altough often confused
)