We can ask: how much information does the image contain? A simple answer is: 5000x3166 pixels, 3 channels per pixel, 1 byte per channel per pixel, so we have 5000*3166*3 = 47.48 million bytes.
But most of that data is not derived from the original photograph, as taken by a photographer. Most of that data comes from the exact sizes and shapes of the black and white dots.
The black and white dots are at intervals around 8.8 pixels. So how many dots in the total image? 5000*3166/8.8/8.8 = 204416 dots. Perhaps each dot has 256 different level, so one byte per dot, so we really have only 204416 bytes of original data.
Put this another way, the real resolution is 5000/8.8 wide and 3166/8.8 high, 568x360 pixels. Blowing those up to 30x20 inches will look blurred. Various process can be used to create the impression of greater sharpness.
Personally, I think there is great charm in enlarged screened lithographed photos, without attempting to “correct” the screening.