Arithmetic properties for two restricted partitions modulo powers of 5

Let p(k)(,3)(n) count the number of 2-color partition triples of n where one of the colors appears only in parts that are multiples of k and B-k,B-l(n) denote the number of (k, l)-regular bipartitions of n. In this paper, we prove two infinite families of congruences modulo 5 for p(5,3)(n), three infinite families of congruences modulo powers of 5 for p(25,3)(n), and six infinite families of congruences modulo powers of 5 for B-5,B-25(n). For instance, for any integers n >= 0 and alpha >= 1, we have and