To clarify, there do exist closed form solutions for quintic functions; they just cannot be expressed using rationals and a limited set of operations of additio

To clarify, there do exist closed form solutions for quintic functions; they just cannot be expressed using rationals and a limited set of operations of additions, subtractions, multiplications, divisions, and root extractions. However, if you do not limit yourself to those operations, there do exist closed form solutions to quintics. See [1] for a few examples. [1] https://mathworld.wolfram.com/QuinticEquation.html https://mathworld.wolfram.com/QuinticEquation.html