An odd-parameter supercongruence for a terminating hypergeometric sum

Let $r\leq 1$ be an odd integer coprime with $5$, and let $p$ be an odd prime such that $p\equiv r\pmod{5}$ and $p\geq (5-3r)/2$. Then the proposed supercongruence.

$$\sum_{k=0}^{p-1}(10k+r)\frac{(\frac{r}{5})_k^5}{(1)_k^5}\equiv\frac{p\Gamma_p(\frac r5)^4}{\Gamma_p(\frac{2r}5)^2\Gamma_p(\frac12+\frac{3r}{10})\Gamma_p(\frac12-\frac r{10})^3}\sum_{k=0}^{(1-r)/2}\frac{(\frac{r-1}{2})_k(\frac r5)_k^3}{(1)_k(\frac{2r}5)_k^2(\frac12+\frac{3r}{10})_k}\pmod{p^5}.$$

This is presented as an open conjecture motivated by a preceding theorem and numerical evidence; its validity remains unresolved in the source.