Using 420pb-1 of data collected on the Υ(5S) resonance with the CLEO III detector, we reconstruct B mesons in 25 exclusive decay channels to measure or set upper limits on the decay rate of Υ(5S) into B meson final states. We measure the inclusive B cross section to be σ(Υ(5S) →BB̄(X))=(0.177±0.030±0.016)nb and make the first measurements of the production rates of σ(Υ(5S)→B *B̄*)=(0.131±0.025±0.014)nb and σ(Υ(5S) →BB̄*)=(0.043±0.016±0.006)nb, respectively. We set 90% confidence level limits of σ(Υ(5S)→BB̄)<0.038nb, σ(Υ(5S)→B(*)B̄(*)π)<0.055nb and σ(Υ(5S)→BB̄ππ)<0.024nb. We also extract the most precise value of the Bs* mass to date, M(Bs*)=(5411.7±1. 6±0.6)MeV/c2.