Close binary interactions may play a critical role in the formation of the rapidly rotating Be stars. Mass transfer can result in a mass gainer star spun up by the accretion of mass and angular momentum, while the mass donor is stripped of its envelope to form a hot and faint helium star. Far-UV spectroscopy has led to the detection of about 20 such binary Be+sdO systems. Here we report on a 3 yr program of high-quality spectroscopy designed to determine the orbital periods and physical properties of five Be binary systems. These binaries are long orbital period systems with P = 95-237 days and small semiamplitude K (1) < 11 km s(-1). We combined the Be star velocities with prior sdO measurements to obtain mass ratios. A Doppler tomography algorithm shows the presence of the He ii lambda 4686 line in the faint spectrum of the hot companion in four of the targets. We discuss the observed line variability and show evidence of phase-locked variations in the emission profiles of HD 157832, suggesting a possible disk spiral density wave due to the presence of the companion star. The stripped companions in HD 113120 and HD 137387 may have a mass larger than 1.4 M (circle dot), indicating that they could be progenitors of Type Ib and Ic supernovae.