Thanks for the correction.
It seems that all the layman’s explanations on Galois theory i have seen have been simplified to the point of being technically wrong, as well as underselling it.
So it's a bit stronger than the term "closed formula" implies. You can then show explicit examples of degree 5 polynomials which don't fulfill this condition, prove a quantitative statement that "almost all" degree 5 polynomials are like this, explain the difference between degree 4 and 5 in terms of group theory, etc.