Andrews-Beck type congruences modulo arbitrary powers of 5 for 2-colored partitions

Recently, Andrews proved two conjectures on a partition statistic introduced by Beck. Chern established some results on weighted rank and crank moments and proved many Andrews-Beck type congruences. Motivated by Andrews and Chern's work, Lin, Peng and Toh introduced a partition statistic of k-colored partitions NBk(r,m,n) which counts the total number of parts of the first component in each k-colored partition pi of n with crank(k)(pi) congruent to r modulo m and proved many congruences for NBk(r,m,n). Very recently, Du and Tang proved a number of Andrews-Beck type congruences for NBk(r,m,n) and confirmed all conjectures posed by Lin, Peng and Toh. Motivated by their work, we establish the generating functions of NB2(r, 5,n) -NB2(5 - r, 5,n) and prove several families of congruences modulo arbitrary powers of 5 for NB2(r, 5,n). In particular, we generalize a congruence modulo 5 for NB2(r, 5,n) due to Lin, Peng and Toh.