Algorithm for finding 5 unknowns?

Question

Algorithms

We change the rating system on the site (the product can be rated from 1 to 5) From the input data, only the sum of the ratings and their number. Task: Approximately select a coefficient for each assessment. That is, for example, we have the sum of ratings 23 and the number of ratings 6. The algorithm must find a coefficient for rating 5 equal to 4 ratings, for rating 2 find 1 rating and one rating in 1. Help with finding a solution.

Answer 1

Bust on the forehead

[ 1, 1, 1, 1, 1, 1 ]
...
[ 5, 5, 5, 5, 2, 1 ]

On the contrary, you can take the maximum estimates [ 5, 5, 5, 5, 5, 5 ]and reduce the last element.