A fifth-order q-supercongruence

Let $m$ and $n$ be positive integers with $n\equiv1\;\allowbreak(\operatorname{mod}4)$, and let $(a;q)_k$ denote the q-shifted factorial. The fifth-order q-supercongruence conjecture.

$$\sum_{k=0}^{mn-1}(-1)^k[4k+1]\frac{(q;q^2)_k^4(q^2;q^4)_k}{(q^2;q^2)_k^4(q^4;q^4)_k}q^k \equiv [n]\frac{(q^2;q^4)_{(n-1)/4}^2}{(q^4;q^4)_{(n-1)/4}^2}\sum_{k=0}^{m-1}(-1)^k(4k+1)\frac{(\frac12)_k^5}{k!^5}\;\allowbreak(\operatorname{mod}\Phi_n(q)^3).$$

The $m=1$ case was previously given by the author; the conjecture is described as a simplified version of earlier conjectures.