If Chase runs 5 miles and 60 minutes, how far will he run in three hours if he continues to run at the same rate

If Chase runs 5 miles in 60 minutes, then he runs at a rate of 5/60 = 1/12 miles per minute.

Thus, in three hours (which is equal to 3 x 60 = <<3*60=180>>180 minutes), he will run 1/12 x 180 = <<1/12*180=15>>15 miles. Answer: \boxed{15}.