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The 2-color partitions may be considered as an extension of regularpartitions of a natural number $n$, with $p_{k}(n)$ defined as the number of2-colored partitions of $n$ where one of the 2 colors appears only in partsthat are multiples of $k$. In this paper, we record the completecharacterization of the modulo 5 congruence relation $p_{k}(25n + 24 - k)\equiv 0 \pmod{5}$ for $k \in \{1, 2, \ldots, 24\}$, in connection with the2-color partition function $p_k(n)$, providing references to existing resultsfor $k \in \{1, 2, 3, 4, 7, 8, 17\}$, simple proofs for $k \in \{5, 10, 15,20\}$ for the sake of completeness, and counter-examples in all the remainingcases. We also propose an alternative proof in the case of $k = 4$, withoutusing the Rogers-Ramanujan ratio, thereby making the proof considerably simplercompared to the proof by Ahmed, Baruah and Ghosh Dastidar (JNT 2015).

Some Observations on Modulo 5 Congruences for 2-Color Partitions