We have obtained accurate near-infrared photometry of the tip of the red giant branch (TRGB) in the Local Group galaxies Sculptor, NGC?6822, NGC?3109, IC?1613, and WLM. We have used the derived TRGB magnitudes together with the absolute magnitude calibration of the near-infrared TRGB magnitude of Valenti et?al. to determine the distances of these five galaxies. The statistical errors in the distance moduli are typically 4%. The systematic uncertainties are dominated by the knowledge of the mean metallicities of the red giant branches and are in the range of 5%-8%. We observe a slight (2%) systematic difference between the distances derived from the J and K bands, respectively, which is within the 1σ errors of the distances. We compare the new distances derived in this paper with other recent distance determinations for our target galaxies and find excellent agreement. In particular, the near-infrared TRGB distances to the four dwarf irregular galaxies in the sample agree to better than 5% in each case with their Cepheid distances obtained from infrared photometry, indicating that there is no appreciable systematic offset between these two fundamental techniques using old and young stellar populations, respectively.
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