The Abel–Ruffini theorem is a result in algebra that states there is no general solution in radicals to polynomial equations of degree five or higher. In other words, it is impossible to express the roots of a general polynomial of degree five or greater using only radicals (i.e., through a finite sequence of operations involving addition, subtraction, multiplication, division, and taking roots).

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Abel-Ruffini theorem by Ciro Santilli 37 Updated +Created
Video 1.
But why is there no quintic formula? by MathKiwi
. Source. 10 minutes, that's about the right length, well done.