  Ramanujan recorded five interesting q-series identities in a section that is
not as systematically arranged as the other chapters of his second notebook.
These five identities do not seem to have acquired enough attention. Recently,
Dixit and the third author found a one-variable generalization of one of the
aforementioned five identities. From their generalized identity, they were able
to derive the last three of these q-series identities, but didn't establish the
first two. In the present article, we derive a one-variable generalization of
the main identity of Dixit and the third author from which we successfully
deduce all the five q-series identities of Ramanujan. In addition to this, we
also establish a few interesting weighted partition identities from our
generalized identity. In the mid 1980's, Bressoud and Subbarao found an
interesting identity connecting the generalized divisor function with a
weighted partition function, which they proved by means of a purely
combinatorial argument. Quite surprisingly, we found an analytic proof for a
generalization of the identity of Bressoud and Subbarao, starting from the
fourth identity of the aforementioned five q-series identities of Ramanujan.
