Rescaling to get 5point distribution?

#1
When creating a scorecard, different categories(6) 5 are currently being rescaled to determine their distribution rating.

Is it correct to rescale the raw scores to fit it in a 5 point distribution?

The Rescaling formula used is the attached photo.

The 'goal' is to always fit the data into a 5 distribution of Rating(Satisfactory, unsatisfactory, meeting expectations, exceeds, exceptional)