  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,
$$s\left(2\cdot 5^{2\alpha-1}n+5^{2\alpha-1}\right)\equiv 0
\pmod{5^{\alpha}}.$$
