Conjectured period-five sign patterns for coefficients of Rogers-Ramanujan products

Let $R(q)$ denote the Rogers–Ramanujan continued fraction, and define integer sequences $A(n)$, $B(n)$, and $D(n)$ by

$$\frac{1}{R^5(q)}=\sum_{n\geq 0}A(n)q^n,\qquad R^5(q)=\sum_{n\geq 0}B(n)q^n,\qquad \frac{R(q^5)}{R^5(q)}=\sum_{n\geq 0}D(n)q^n.$$

Conjectured sign pattern. For all integers $n\geq0$,

$$A(5n)<0,\qquad B(5n)<0,\qquad D(5n+1)>0.$$

An affirmative answer, together with the stated sign-pattern theorems for the other residue classes, would prove that the signs of $A(n)$, $B(n)$, and $D(n)$ are periodic with period $5$. The conjecture is based on numerical observation, and its status is unresolved in the supplied text.