Guillera–Zudilin-type supercongruence for a fifth-power hypergeometric sum

Let $p$ be an odd prime, let $r$ be a positive integer, and let $\delta\in\{1,2\}$. Guillera–Zudilin-type conjecture.

$$\sum_{n=0}^{(p^r-1)/\delta}\frac{\left(\frac12\right)^5_n}{n!^5}(10n^2+6n+1)(-4)^n\equiv p^{2r}\pmod{p^{2r+3}}.$$

The paper states that this stronger modulus cannot be proved by its method; the surrounding theorem establishes a weaker, piecewise congruence modulo $p^{r+4}$.