  In this paper we study an $AdS_5$ solution constructed using non-Abelian
T-duality, acting on the Klebanov-Witten background. We show that this is dual
to a linear quiver with two tails of gauge groups of increasing rank. The field
theory dynamics arises from a D4-NS5-NS5' brane set-up, generalizing the
constructions discussed by Bah and Bobev. These realize $\mathcal{N}=1$ quiver
gauge theories built out of $\mathcal{N}=1$ and $\mathcal{N}=2$ vector
multiplets flowing to interacting fixed points in the infrared. We compute the
central charge using $a$-maximization, and show its precise agreement with the
holographic calculation. Our result exhibits $n^3$ scaling with the number of
five-branes. This suggests an eleven-dimensional interpretation in terms of
M5-branes, a generic feature of various $AdS$ backgrounds obtained via
non-Abelian T-duality.
