1-Shell totally symmetric plane partitions (TSPPs) modulo powers of 5

Let $s(n)$ be the number of 1-shell totally symmetric plane partitions (TSPPs) of $n$. In this paper, an infinite family of congruences modulo powers of $5$ for $s(n)$ will be deduced through an elementary approach. Namely, $$s(2\cdot 5^{2\alpha -1}n+5^{2\alpha -1})\equiv 0(\mathrm{m}\mathrm{o}\mathrm{d}{5}^{\alpha })\mathrm{.}$$