I don't understand why so many heights are shown. Usually the mature plant height is always shown, i.e. 5 - 7 m. But when looking here at the height, so many are given that I don't know which is the correct range for a particular palm.
Couple possibilities--one is that all plants will have a range of mature heights. The way Plant Files works, there are boxes to represent a range of heights, for example one box maybe for 1-3 meters, another for 3-5 m, etc. If the Plant Files boxes don't match up exactly with the plant's height range, whoever made the entry would have to check off multiple boxes in order to cover the range in height. So it's possible because of that to end up with 3 or 4 different height range boxes checked.
The second possibility is that there can be mistakes--Plant Files relies on user submitted data so there can definitely be errors. If you have data from other reputable sites that gives a different height range than what is shown in Plant Files, you can use the "report an error" button on the Plant Files page to let admins know about the mistake.