  It has been proposed that the globular cluster-like system Terzan 5 is the
surviving remnant of a primordial building block of the Milky Way bulge, mainly
due to the age/metallicity spread and the distribution of its stars in the
$\alpha$-Fe plane. We employ Sloan Digital Sky Survey (SDSS-IV) data from the
Apache Point Observatory Galactic Evolution Experiment (APOGEE 2) to test this
hypothesis. Adopting a random sampling technique, we contrast the abundances of
10 elements in Terzan 5 stars with those of their bulge field counterparts with
comparable atmospheric parameters, finding that they differ at statistically
significant levels. Abundances between the two groups differ by more than
1$\sigma$ in Ca, Mn, C, O, and Al, and more than 2$\sigma$ in Si and Mg. Terzan
5 stars have lower [$\alpha$/Fe] and higher [Mn/Fe] than their bulge
counterparts. Given those differences, we conclude that Terzan 5 is not the
remnant of a $major$ building block of the bulge. We also estimate the stellar
mass of the Terzan 5 progenitor based on predictions by the Evolution and
Assembly of GaLaxies and their Environments (EAGLE) suite of cosmological
numerical simulations, concluding that it may have been as low as
$\sim3\times10^8$ M$_\odot$ so that it was likely unable to significantly
influence the mean chemistry of the bulge/inner disk, which is significantly
more massive ($\sim10^{10}$ M$_\odot$). We briefly discuss existing scenarios
for the nature of Terzan 5 and propose an observational test that may help
elucidate its origin.
