  Since the discovery of high-temperature superconductivity in the copper oxide
materials, there have been sustained efforts to both understand the origins of
this phase and discover new cuprate-like superconducting materials. One prime
materials platform has been the rare-earth nickelates and indeed
superconductivity was recently discovered in the doped compound
Nd$_{0.8}$Sr$_{0.2}$NiO$_2$. Undoped NdNiO$_2$ belongs to a series of layered
square-planar nickelates with chemical formula Nd$_{n+1}$Ni$_n$O$_{2n+2}$ and
is known as the 'infinite-layer' ($n = \infty$) nickelate. Here, we report the
synthesis of the quintuple-layer ($n = 5$) member of this series,
Nd$_6$Ni$_5$O$_{12}$, in which optimal cuprate-like electron filling
($d^{8.8}$) is achieved without chemical doping. We observe a superconducting
transition beginning at $\sim$13 K. Electronic structure calculations, in
tandem with magnetoresistive and spectroscopic measurements, suggest that
Nd$_6$Ni$_5$O$_{12}$ interpolates between cuprate-like and infinite-layer
nickelate-like behavior. In engineering a distinct superconducting nickelate,
we identify the square-planar nickelates as a new family of superconductors
which can be tuned via both doping and dimensionality.
