Quintic polynomial with Galois Group $A_5$ A recent question asks what makes degree 5 special when considering the roots of polynomials with integer coefficients etc. One answer is that the Galois Group of $S_5$ is not solvable. What I am looking for is the most straightforward example (with proof) of a polynomial with integer coefficients and Galois Group $A_5$.
Such an object ought to be standard ... if I ever knew one, I have forgotten it.

You may want to read chapter $\,4\,$ here , page $\,84\,$ in the "ereaders" version.
After some rather messy and annoying calculations, the discriminant of for example the polynomial $\,x^5+20x+16\in\Bbb Q[x]\,$ , which appears in the other answer, is $\,5^2\cdot 80^4\,$ , which is a square in $\,\Bbb Q\,$ and thus its Galois Group is contained in $\,A_5\,$...
