  Let $K_n$ be a tamely ramified cyclic quintic field generated by a root of
Emma Lehmer's parametric polynomial. We give all normal integral bases for
$K_n$ only by the roots of the polynomial, which is a generalization of the
work of Lehmer in the case that $n^4+5n^3+15n^2+25n+25$ is prime number, and
Spearman-Willliams in the case that $n^4+5n^3+15n^2+25n+25$ is square-free.
