Great clear-eyed and cynical take here, I like the spirit of this comment if not all the details/conclusions, but can you provide a link/source for "You can look at historical graphs of fed rate vs unemployment to verify" and the "federal reserve defines the "natural rate of unemployment" as being around 5%" claims?
I think both of these are probably roughly true-ish but by brief Googling I couldn't verify either one.
https://commons.wikimedia.org/wiki/File:Federal_funds_rate_v... <-- that's a graph like what I'm talking about. Notice how the blue tends to go up sharply before the grey recession bars. And this tends to happen right as the red line starts to approach 5%. There's an exception recently because trump was in office demanding that they keep the fed rate low, and I guess they decided to listen to him because he was cutting their taxes. But you can tell they didn't love the guy by the way the media covered him. I'm no fan either, but for different reasons.
That wiki graph does not show what you say. There are multiple place in the curve that don't follow your theory. And by places, I mean for example the stretch from 1980 to 2000.
I think both of these are probably roughly true-ish but by brief Googling I couldn't verify either one.