We present a study of the halo dynamics and mass distributions of the nearby giant elliptical galaxy NGC 5128 using planetary nebulae (PNs) as test particles. Radial velocities of 433 PNs were obtained with multifiber spectrographs on both the Anglo-Australian Telescope (AAT) and the Cerro Tololo Inter-American Observatory (CTIO) 4m telescope. The velocities were measured from the [O III]{lambda}5007 emission line with a typical 1{sigma} error of +/-4km/s and +/-30km/s for the AAT and the CTIO data, respectively. These PNs cover the entire galaxy to a radius of 10kpc and extend along the photometric major axis out to 20kpc. The PN velocity field shows the distinctive characteristics of a triaxial potential: the galaxy's rotation axis is offset from its photometric minor axis by 39+/-10deg; the rotation axis and the line of maximum rotation are likely not orthogonal. We also find that the ordered motions of the stars become more important with increasing radius compared to their random motions. The rotation reaches approximately 100km/s and 50km/s along the photometric major and minor axes, giving a local V/{sigma} ratio of about 1.0 and 0.5, respectively. The aximuthal variation of the velocity dispersion appears to be modulated by rotation, i.e., it reaches a maximum where the largest rotation is observed and drops to a minimum at zero rotation. The amplitude of this modulation is about 20km/s, compared to a mean dispersion velocity of 110km/s. The kinematics of the globular clusters depend on the metallicity. Taking [Fe/H]=-1.0 as the dividing point, the metal-poor clusters do not show any significant rotation. However the metal-rich clusters show both major and minor axis rotation, and the amplitudes of the rotation are similar to that of the PNs. The stellar velocity dispersion measured from absorption-line spectra together with an H{alpha} rotation curve of the dust lane suggest that the stellar orbits are isotropic and the mass-to-light ratio (M/L_B_) is 3.9 in the central region of the galaxy. By applying the isotropic Jeans equation to the observed PN major axis rotation and velocity dispersion, we show that the M/L_B_ increases with radius, suggesting the presence of dark matter in the halo. Within a 25kpc radius, the total mass of the galaxy is 3.1x10^11^M_{sun} and M/L_B=10. The rotation velocity of the recently detected H I ring at a radius of 15kpc confirms our mass model. The misalignment of the rotation axis relative to the photometric minor axis, combined with the knowledge of the dust lane orientation, allows us to uniquely determine the observer's viewing direction. The true shape of the galaxy is nearly spherical yet sufficiently triaxial to impose a distinctive gravitational signature on the kinematics.