Well, enum is needed to ensure you have a fixed number of unique values of the same type.
That's the situation where you'd typically use enum:
public class Finger
public static const THUMB:Finger = new Finger();
public static const INDEX:Finger = new Finger();
public static const MIDDLE:Finger = new Finger();
public static const RING:Finger = new Finger();
public static const LITTLE:Finger = new Finger();
Because well, there won't be any more fingers... well, who knows, but, it doesn't seem like that
So, now, if you'd have to choose a finger, then you'd definitely choose one of the existing fingers - this would spare you validating string or numeric input to see if the number is not negative and less then 5, or that the string which is a name of the finger is exactly the same as one of the predefined finger names.
So it is in the scope of your application: there probably won't be any more seasons, or, even if there will be, they will be few (not dynamically defined) - that's why I thought that enum would be better.