The invariants of orthogonal group actions

Let F_q be the finite field of order q, an odd number, Q a non-degenerate quadratic form on [formula omitted]O(n, Q) the orthogonal group defined by Q. Regard O(n, Q) as a linear group of F_q -automorphisms acting linearly on the rational function field F_q(x₁, …, x_n). We shall prove that the invariant subfield F_q(x₁,…, x_n)^{O(n, Q)} is a purely transcendental extension over F_q for n = 5 by giving a set of generators for it.