Definition:Quintic Equation

Definition
Let $f \left({x}\right) = a x^5 + b x^4 + c x^3 + d x^2 + e x + f$ be a polynomial function of degree $5$ over a field $k$.

Then the equation $f \left({x}\right) = 0$ is the general quintic equation over $k$.

Also see

 * Abel-Ruffini Theorem, which proves that, in general, a quintic equation can not be solved analytically.