  We study a $D_p$-brane in a parallelizable NS-NS background. The article
starts with a brief review of the non-associative deformation of $D$-brane
worldvolume in presence of torsion \cite{cornalba}. We suggest an alternative
form and heuristic derivation of the open string metric for weakly curved
backgrounds, by promoting the constant two-form in the flat space formula to a
dynamical two-form and then Taylor expanding the bulk fields in Riemann Normal
Coordinates at the origin. For weakly curved backgrounds, terms only upto the
leading order in the NS-NS field strength or torsion contribute. This formalism
differs from the author's earlier works in a collaboration \cite{richa}. We use
the open string metric proposed in this paper to determine the deformation of
$D_5$-brane for a particular NS-NS background. It turns out that a spherical
$D_5$-brane with torsion acts like an extremal black 5-brane in the limit of
radius $r \rightarrow 0$. This is an interesting case of gauge/gravity duality
with an intractable non-commutative and non-associative gauge theory on a
$D_p$-brane with torsion, which is equivalent to a simpler and ordinary gravity
theory on the extremal black brane.
