An automatic system for testing up to 32 photomultiplier tubes (PMT's) simultaneously under single photon counting conditions has been used to measure characteristics of more than 1000 five inch diameter hemispherical PMT's for use in the Irvine-Michigan-Brookhaven (IMB) Proton Decay Experiment. 2400 of these tubes (EMI 9870B or 9834B) will be used in an 8000 m3 water Cerenkov detector now under construction in the Morton-Norwich Salt Mine at Fairport Harbor, Ohio. The PMT test system is described and results of testing the first half of the PMT complement are presented. In general we find that the tube characteristics have smaller fluctuations than expected. On the basis of our experience, we make suggestions as to new industry standards for PMT's to be used in fast particle counting.