Some new congruence identities of general partition for $p_r(n)$

In the present work, we deduce some new congruences modulo 3 and 5 for $p_r(n)$, where $r \in \{-(3\lambda+3), -(5\lambda+3) \mid \lambda \text{ is any non-negative integer}\}$. Our emphasis throughout this paper is to exhibit the use of $q$-identities to generate the congruences for $p_r(n)$.