We present Subaru/Faint Object Camera and Spectrograph and Keck/Deep Imaging Multi-Object Spectrometer medium-resolution spectroscopy of a tidally disrupting Milky Way (MW) globular cluster Palomar 5 (Pal 5) and its tidal stream. The observed fields are located to cover an angular extent of ~17{deg} along the stream, providing an opportunity to investigate a trend in line-of-sight velocities (V_los_) along the stream, which is essential to constrain its orbit and underlying gravitational potential of the MW's dark matter halo. A spectral fitting technique is applied to the observed spectra to obtain stellar parameters and metallicities ([Fe/H]) of the target stars. The 19 stars most likely belonging to the central Pal 5 cluster have a mean V_los_ of -58.1+/-0.7km/s and metallicity [Fe/H]=-1.35+/-0.06dex, both of which are in good agreement with those derived in previous high-resolution spectroscopic studies. Assuming that the stream stars have the same [Fe/H] as the progenitor cluster, the derived [Fe/H] and V_los_ values are used to estimate the possible V_los_ range of the member stars at each location along the stream. Because of the heavy contamination of the field MW stars, the estimated V_los_ range depends on prior assumptions about the stream's V_los_, which highlights the importance of more definitely identifying the member stars using proper motion and chemical abundances to obtain unbiased information of V_los_ in the outer part of the Pal 5 stream. The models for the gravitational potential of the MW's dark matter halo that are compatible with the estimated V_los_ range are discussed.