Some animals seem to be just more in "the spotlight" then others. My lions for example hit five stars pretty fast. My warthogs have sometimes five stars aswell. I think the following things impact this:

1: Stats of the animals, Goldies get faster 5 stars.
2: Species themselves, Lions are more impressive then warthogs for example.
3: Quality of food
4: The amount of breeding
5: A habitat that is very accessable to the population ( No super big habitats where guests can't see the animals as much as they would like)
6: How much donations the animal recieve. For example my warthogs recieve nearly as much donations as my lions, people just love that they can constantly see them upon very close.