Winamp 3 was a total rewrite of Winamp using a completely bespoke fully skinnable GUI system. All Winamp 3 skins were what would eventually be called "modern" skins.

However, Winamp 3 also had performance issues, and ultimately the negative reaction to it led Nullsoft to kill most of Winamp 3. The GUI code (and associated APIs mentioned in this blog post) were hacked into the older Winamp 2.x codebase and given the "modern skin" name. (The name "Winamp 5" was supposed to be a play on 2 (codebase) + 3 (modern skins) = 5)

There were also “other” reasons to skip version number 4: https://jordaneldredge.com/notes/winamp-4-skin/