Has a Copa America game ever ended 5-2?
Yes. Copa America has seen a final score of 5-2 5 times. It first happened on December 6, 1925, when Brazil beat Paraguay, and most recently on July 1, 1989, when Paraguay beat Peru.
That makes 5-2 the 21st most common final score out of 36 that have ever occurred in Copa America. One point away, 6-2 has happened 1 times and 5-3 has happened 4 times. At one point the score disappeared for 30 years, between 1959 and 1989.