We present spectrograms of the faint V –drop ( V _ { 606 } = 28.1 ,I _ { 814 } = 25.6 ) galaxy pair HDF 3–951.1 and HDF 3–951.2 obtained at the Keck II Telescope . Fernández–Soto , Lanzetta , & Yahil ( 1998 ) derive a photometric redshift of z _ { ph } = 5.28 ^ { +0.34 } _ { -0.41 } ( 2 \sigma ) for these galaxies ; our integrated spectrograms show a large and abrupt discontinuity near 7710 \pm 5 Å . This break is almost certainly due to the Ly \alpha forest as its amplitude ( 1 - f _ { \nu } ^ { short } / f _ { \nu } ^ { long } > 0.87 , 95 \% confidence limit ) exceeds any discontinuities observed in stellar or galaxian rest–frame optical spectra . The resulting absorption–break redshift is z = 5.34 \pm 0.01 . Optical/near–IR photometry from the HDF yields an exceptionally red ( V _ { 606 } - I _ { 814 } ) color , consistent with this large break . A more accurate measure of the continuum depression blueward of Ly \alpha utilizing the imaging photometry yields D _ { A } = 0.88 . The system as a whole is slightly brighter than L _ { 1500 } ^ { * } relative to the z \sim 3 Lyman break population and the total star formation rate inferred from the UV continuum is \approx 22 h _ { 50 } ^ { -2 } { M _ { \odot } } yr ^ { -1 } ( q _ { 0 } = 0.5 ) assuming the absence of dust extinction . The two individual galaxies are quite small ( size scales \mathrel { \hbox to 0.0 pt { \lower 3.0 pt \hbox { $ \mathchar 536 $ } \hss } \raise 2.0 pt% \hbox { $ \mathchar 316 $ } } 1 h _ { 50 } ^ { -1 } kpc ) . Thus these galaxies superficially resemble the Pascarelle et al . ( 1996 ) “ building blocks ” ; if they comprise a gravitationally bound system , the pair will likely merge in a time scale \sim 100 Myr .