We present spectroscopic confirmation of five galaxy clusters at $1.25 < textit{z} < 1.5$, discovered in the $2500$ deg$^{2}$ South Pole Telescope Sunyaev-Zeldovich (SPT-SZ) survey. These clusters, taken from a mass-limited sample with a nearly redshift independent selection function, have multi-wavelength follow-up imaging data from the X-ray to near-infrared, and currently form the most homogeneous massive high-redshift cluster sample known. We identify $44$ member galaxies, along with $25$ field galaxies, among the five clusters, and describe the full set of observations and data products from Magellan/LDSS3 multi-object spectroscopy of these cluster fields. We briefly describe the analysis pipeline, and present ensemble analyses of cluster member galaxies that demonstrate the reliability of the measured redshifts. We report $textit{z} = 1.259, 1.288, 1.316, 1.401$ and $1.474$ for the five clusters from a combination of absorption-line (Ca II H$&$K doublet - $3968,3934$ {AA}) and emission-line ([OII] $3727,3729$ {AA}) spectral features. Moreover, the calculated velocity dispersions yield dynamical cluster masses in good agreement with SZ masses for these clusters. We discuss the velocity and spatial distributions of passive and [OII]-emitting galaxies in these clusters, showing that they are consistent with velocity segregation and biases observed in lower redshift SPT clusters. We identify modest [OII] emission and pronounced CN and H$delta$ absorption in a stacked spectrum of $28$ passive galaxies with Ca II H$&$K-derived redshifts. This work increases the number of spectroscopically-confirmed SZ-selected galaxy clusters at $textit{z} > 1.25$ from three to eight, further demonstrating the efficacy of SZ selection for the highest redshift massive clusters, and enabling detailed study of these systems.
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