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Active galactic Nuclei (AGNs) with their relativistic jets pointed toward the observer, are a class of luminous gamma-ray sources commonly known as blazars. The study of this source class is essential to unveil the physical processes powering these extreme jets, to understand their cosmic evolution, as well as to indirectly probe the extragalactic background light. To do so, however, one needs to correctly classify and measure a redshift for a large sample of these sources. The Third Fermi-LAT Catalog of High-Energy Sources (3FHL) contains $1212$ blazars detected at energies greater than 10 GeV. However, $\sim$25% of these sources are unclassified and $\sim$56% lack redshift information. To increase the optical completeness of blazars in the 3FHL catalog, we devised an optical spectroscopic follow-up campaign using 4 $m$ and 8 $m$ telescopes. In this paper, we present the results of the last part of this campaign, where we observed 5 blazars using the 8 $m$ Gemini-S telescope in Chile. We report all 5 sources to be classified as BL Lacs, a redshift lower limit for 2 sources, and featureless spectra for the remaining 3 sources. We also performed a one-zone leptonic fit to the two sources with the redshift lower limits.