We report the GALLEX solar neutrino results for the measuring period GALLEX III, the period from 12 October 1994-4 October 1995. Counting for these runs was completed on 29 March 1996. The GALLEX III result (14 runs) is [53.9 ± 10.6(stat.) ± 3.1 (syst.)] SNU (1σ). This is 15.8 SNU below but statistically compatible with the new combined result for GALLEX (I+II+III) (53 runs), which is [69.7 ± 6.7 (stat.) + 3 . 9 - 4 . 5 (syst.)] SNU (1σ) or (69.7 + 7 . 8 - 8 . 1 ) SNU with errors quadratically added. We also give the preliminary result from our second 5 1 Cr-source experiment: the measured detector response is 83±10% of expectation. The combined result from both GALLEX 5 1 Cr-source experiments is 92±8% of expectation.