We obtained adaptive-optics assisted SINFONI observations of the central regions of the giant elliptical galaxy NGC5419 with a spatial resolution of 0.2 arcsec ($approx 55$ pc). NGC5419 has a large depleted stellar core with a radius of 1.58 arcsec (430 pc). HST and SINFONI images show a point source located at the galaxys photocentre, which is likely associated with the low-luminosity AGN previously detected in NGC5419. Both the HST and SINFONI images also show a second nucleus, off-centred by 0.25 arcsec ($approx 70$ pc). Outside of the central double nucleus, we measure an almost constant velocity dispersion of $sigma sim 350$ km/s. In the region where the double nucleus is located, the dispersion rises steeply to a peak value of $sim 420$ km/s. In addition to the SINFONI data, we also obtained stellar kinematics at larger radii from the South African Large Telescope. While NGC5419 shows low rotation ($v < 50$ km/s), the central regions (inside $sim 4 , r_b$) clearly rotate in the opposite direction to the galaxys outer parts. We use orbit-based dynamical models to measure the black hole mass of NGC5419 from the kinematical data outside of the double nuclear structure. The models imply M$_{rm BH}=7.2^{+2.7}_{-1.9} times 10^9$ M$_{odot}$. The enhanced velocity dispersion in the region of the double nucleus suggests that NGC5419 possibly hosts two supermassive black holes at its centre, separated by only $approx 70$ pc. Yet our measured M$_{rm BH}$ is consistent with the black hole mass expected from the size of the galaxys depleted stellar core. This suggests, that systematic uncertainties in M$_{rm BH}$ related to the secondary nucleus are small.