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.

Here are some found by computer search
$$x^5 - 55x - 88$$
$$x^5 - 55x + 88$$
$$x^5 + 20x - 16$$
$$x^5 + 20x + 16$$
$$x^5 + 95x - 76$$
$$x^5 + 95x + 76$$

$$x^5 + 3x^3 + 5x - 10$$
$$x^5 + 3x^3 + 5x + 10$$
$$x^5 + 6x^3 - 7x - 8$$
$$x^5 + 6x^3 - 7x + 8$$
$$x^5 + 10x^3 - 10x - 4$$
$$x^5 + 10x^3 - 10x + 4$$

$$x^5 - x^4 + x^3 + 2x^2 + x - 1$$
$$x^5 + x^4 + x^3 - 2x^2 + x + 1$$
