[DetroitSky]

It ultimately depends on the definition of "skyscraper", which varies from country to country or even town to town. I was recently in Hoopeston, Illinois, about 2.5 hours from Chicago, and discovered a 5 story terra cotta clad office building in a downtown that was otherwise stereotypical small town America. Upon googling the history of the building, I found a comment on its Facebook page from a local calling it "Hoopeston's only skyscraper".

Point being a 5 story building in a town dominated by 1-3 story buildings could be called a "skyscraper", but that building would barely stand out in Chicago. Other, less developed countries, like Haiti, consider a 10 story building a skyscraper, but again in Chicago or NYC that's nothing.

And then it depends on the structure of the building, steel or otherwise. But if a steel framed tall building is a skyscraper, does that mean tall wood framed buildings aren't skyscrapers?

Like Steely Dan said, there isn't a first skyscraper, but many buildings' combined firsts created what we now consider skyscrapers.