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I am confused as to when the best time is to change a photo's resolution from 76 to 300 for printing out a 5 X 7 High Quality print. Do I do it before or after cropping? Do I do it at all and just change the size to 5 X 7 from it's original size of 19 X 25 inches at 76 resolution and let the program do the calculating? I guess I'm confused as to which setting determines the final quality?

It is best to think in pixels.

You say your camera takes photos 19x25 @ 76dpi
That is (19x76)x(25x76) pixels
=1444x1900 pixels

For a 5x7 print at 300dpi you need
(5x300)x(7x300) pixels
=1500x2100 pixels
Crop, keeping the aspect ratio at 1500x2100
Then scale to 1500x2100 if necessary