I can only try-
We discussed once (I’m too lazy to link it) that equations to a mathematician are like tools for a plumber. When you are shown a solution it looks easy but without training you wouldn’t know which tools to use.
This, you said, was why plumbers charge so much- they have the experience to look at a problem and fix it. So, in essence you are paying for his experience and not his work.
As far as earning an Erd?s number of 5- there was a rumor that Hank Aaron earned an Erd?s number of 1- by signing a baseball with Paul Erd?s.