Third Borwein conjecture on coefficients of quintic Borwein polynomials

Let $v_n(q)$, $\phi_n(q)$, $\chi_n(q)$, $\psi_n(q)$, and $\omega_n(q)$ be the polynomials defined by

$$\frac{(q;q)_{5n}}{(q^5;q^5)_n}=v_n(q^5)-q\phi_n(q^5)-q^2\chi_n(q^5)-q^3\psi_n(^5)-q^4\omega_n(q^5).$$

Third Borwein conjecture. Each of $v_n(q)$, $\phi_n(q)$, $\chi_n(q)$, $\psi_n(q)$, and $\omega_n(q)$ has non-negative coefficients. This is one of the sign-pattern conjectures for Borwein polynomials, formalized by Andrews; the displayed source statement contains the argument $\psi_n(^5)$ exactly as written, and the supplied source does not state whether the conjecture has been resolved.