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)
That's how I remember it as well. I think I ran Winamp 3 in Wine a year or two ago and whatever I was running definitely supported modern skins. Perhaps these Winamp 5 skins are a different beast.
Was it really since Winamp 5? IIRC, I installed them on Winamp 3.
Edit: I just fell into a nostalgia spiral reading Winamp forums. It still has posts from 2000.