Basis of a finite field extension

Question

The splitting field of $p(x)=x^4- x^2-3 \in\mathbb{F}_5[x]$ is $\mathbb{F}_5(\sqrt{3+\sqrt2} )$ because every finite field extension is normal and $\sqrt{3+\sqrt2}$ is a root of the irreducible polynomial. Now my question is how do I determine a Basis for this extension.