There is no such thing as Skilled 15, Kiriak.
It's either Gathering Level 25 or Skilled 5 (Beginner 10 + Apprentice 10 + Skilled 5 = Gathering Level of 25)
Also, the Shining Steel Pickaxe requires Skilled 5. Here's an in-game screenshot so you don't have to take my word for it. http://imgur.com/x80L4YF