There are several parts of this question. There are some similar questions out threre, so I'll be more specific.
1) Your Data:
5184 x 3456 px.
20 x 16 inches.
Note that I added the actual units.
This is important. Resolution is a relationship between 2 units. 1 unit is of information (A), one is for dimension (B).
In this case the unit "A" is pixel and the unit "B" are inches. Unit B can be for example centimeters.
2) The proportion. You define that using the crop tool.
20 x 16 = 1.25. The width is 1.25 times greater than the height.
So 3456 x 1.25 = 4320. You need to crop your image that size.
From there you do not to do anithinganything. The file size is good enough. But here are some more numbers.
4320 px on 20 inches (the units again) are 4320/20 = 216. This is your photo's resolution printed at that phisical size. 216 pixels on each inch... pixels per inch or ppi. UNITS AGAIN!
3) 72, 300 and 600 are some ppi "standards".
The 300 ppi is the most important "standard for comercial printing, like a magazine. But even this one is not carved in stone.
600 ppi is for a special case of image that is only pure black and pure white. No gray or color, that is called a monochromathic image.
72 ppi... That is a pointless historical information that only confuses web designers.
There are other values. But that is an offtopic for photography. That is a designers issue.
Returning to the Photographers point of view. A photo will be fine if it is on the 150 - 300 ppi.
You do not need more than 300. But sometimes, where you are printing wall sized photos, you could get away with lets say 50 ppi or less.
Important note.
The correct unit for you is ppi, not dpi.
The dpi is another diferent relationship to mesure a printer's resolution, not a photo resolution. A printer is defined on how many dots of ink can deliver on an inch... dots per inch.