What you call a plot point I know as a crisis, also major turn. Five crises: inciting crisis, realization crisis, climax crisis, tragic crisis, and transformation crisis. Each is based on addressing a central dramatic complication, which is a problem wanting satisfaction.
The synopsis you give suggests to me the problem is a bad guy. A villain. For a who-done-it mystery, a murderer is the villain but the problem wanting satisfaction is finding out who done it, the murderer. I don't see what makes your bad guy a villain or a problem wanting satisfaction.
A basic outline of a five-act structure, each part roughly the same in word count and similar to a three-act or four-act structure:
Exposition act, introduction scenes, primarily of the problem wanting satisfaction, minor turn
Inciting crisis bridge scene, major turn
Rising action act, scene one, minor turn
Rising action act, scene two, minor turn
Rising action act, scene three, minor turn
Realization crisis bridge scene, major turn
Climax act, entry scene, minor turn
Climax crisis bridge scene, most major turn
Climax act, exit scene, minor turn
Tragic criris bridge scene, major turn
Falling action act, scene one, minor turn
Falling action act, scene two, minor turn
Falling action act, scene three, minor turn
Transformation crisis bridge scene, major turn
Denouement act scenes
I think you've got each scene and act up through the third falling action scene, but shy of the transformation crisis bridge scene and denouement act scenes. A transformation crisis is when a protagonist at last realizes an appreciable change in circumstances due to a central dramatic complication's dramatic action.
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