We have identified two new near-infrared emission lines in the spectra of planetary nebulae (PNe) arising from heavy elements produced by neutron capture reactions: [Te III] 2.1019 $mu$m and [Br V] 1.6429 $mu$m. [Te III] was detected in both NGC 7027 and IC 418, while [Br V] was seen in NGC 7027. The observations were obtained with the medium-resolution spectrograph EMIR on the 10.4m Gran Telescopio Canarias at La Palma, and with the high-resolution spectrograph IGRINS on the 2.7m Harlan J. Smith telescope at McDonald Observatory. New calculations of atomic data for these ions, specifically A-values and collision strengths, are presented and used to derive ionic abundances of Te$^{2+}$ and Br$^{4+}$. We also derive ionic abundances of other neutron-capture elements detected in the near-infrared spectra, and estimate total elemental abundances of Se, Br, Kr, Rb, and Te after correcting for unobserved ions. Comparison of our derived enrichments to theoretical predictions from AGB evolutionary models shows reasonable agreement for solar metallicity progenitor stars of $sim$2 - 4 M$_{odot}$. The spectrally-isolated [Br V] 1.6429 $mu$m line has advantages for determining nebular Br abundances over optical [Br III] emission lines that can be blended with other features. Finally, measurements of Te are of special interest because this element lies beyond the first peak of the s-process, and thus provides new leverage on the abundance pattern of trans-iron species produced by AGB stars.
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