Congruences modulo powers of 5 for the crank parity function (Q6558467)

In order to provide a combinatorial interpretation for Ramanujan's partition congruence modulo \(11\) \textit{G. E. Andrews} and \textit{F. G. Garvan} [Bull. Am. Math. Soc., New Ser. 18, No. 2, 167--171 (1988; Zbl 0646.10008)] introduced the partition statistic ``crank''. Later, \textit{D. Choi} et al. [J. Comb. Theory, Ser. A 116, No. 5, 1034--1046 (2009; Zbl 1228.05044)] established congruences modulo powers of 5 for the crank parity function \( p_C(n) \), which represents the difference between the number of partitions of \( n \) with even crank and those with odd crank, using the theory of modular forms. In this paper, the author presents a completely elementary proof of this family of congruences. Several new congruences modulo small powers of \(5\) are introduced in this context.