The ratio of green tiles to purple tiles in the art class mosaic is 5 to 8 if there were 72 tiles in the design, how many green tiles would there be?

The total ratio of green tiles to purple tiles is 5+8=<<5+8=13>>13.

The fraction representing the number of green tiles is 5/13, and since there were 72 tiles in the design, there would be 5/13*72=<<5/13*72=27.692307692307693>>27.692307692307693 green tiles. Answer: \boxed{28}.