Congruences modulo powers of 5 for two restricted bipartitions

Let B-5(n) denote the number of 5-regular bipartitions of n. We establish some Ramanujan-type congruences like B-5(4n = 3) equivalent to 0 (mod 5) and many infinite families of congruences for B-5(n) modulo higher powers of 5 such as B-5(5(2k-1)n + 2 . 5(2k-1) - 1/3) equivalent to 0 (mod 5(k)). We also apply the same method to obtain some similar results for another type of bipartition function. Meanwhile, we give a new interesting interlinked q-series identity related with Rogers-Ramanujan continued fraction, which answers a question of M. Hirschhorn.