Maximal real subfield of the fifth cyclotomic field ($\mathbb{Q}({\zeta }_5+{\zeta }_5^{-1})=\mathbb{Q}(\sqrt{5})$)

For a primitive fifth root ${\zeta }_5$, the element $s={\zeta }_5+{\zeta }_5^{-1}$ satisfies $s^2+s-1=0$. Thus the fixed field of complex conjugation is