Wide-field photometric data from the Sloan Digital Sky Survey have recently revealed that the Galactic globular cluster Palomar 5 is in the process of being tidally disrupted ( Odenkirchen et al . 2001 ) . Here we investigate the kinematics of this sparse remote star cluster using high resolution spectra from the Very Large Telescope ( VLT ) . Twenty candidate cluster giants located within 6 arcmin of the cluster center have been observed with the UV-Visual Echelle Spectrograph ( UVES ) on VLT-UT2 . The spectra provide radial velocities with a typical accuracy of 0.15 km s ^ { -1 } . We find that the sample contains 17 certain cluster members with very coherent kinematics , two unrelated field dwarfs , and one giant with a deviant velocity , which is most likely a cluster binary showing fast orbital motion . From the confirmed members we determine the heliocentric velocity of the cluster as -58.7 \pm 0.2 km s ^ { -1 } . The total line-of-sight velocity dispersion of the cluster stars is 1.1 \pm 0.2 km s ^ { -1 } ( all members ) or 0.9 \pm 0.2 km s ^ { -1 } ( stars on the red giant branch only ) . This is the lowest velocity dispersion that has so far been measured for a stellar system classified as a globular cluster . The shape of the velocity distribution suggests that there is a significant contribution from orbital motions of binaries and that the dynamical part of the velocity dispersion is therefore still substantially smaller than the total dispersion . Comparing the observations to the results of Monte Carlo simulations of binaries we find that the frequency of binaries in Pal 5 is most likely between 24 % and 63 % and that the dynamical line-of-sight velocity dispersion of the cluster must be smaller than 0.7 km s ^ { -1 } ( 90 % confidence upper limit ) . The most probable values of the dynamical dispersion lie in the range 0.12 \leq \sigma / \mbox { km s$ { } ^ { -1 } $ } \leq 0.41 ( 68 % confidence ) . Pal 5 thus turns out to be a dynamically very cold system . Our results are compatible with an equilibrium system . We find that the luminosity of the cluster implies a total mass of only 4.5 to 6.0 \times 10 ^ { 3 } M _ { \odot } . We further show that a dynamical line-of-sight velocity dispersion of 0.32 to 0.37 km s ^ { -1 } admits a King model that fits the observed surface density profile of Pal 5 ( with W _ { 0 } = 2.9 and r _ { t } = 16 \farcm 1 ) and its mass .