We present a detailed study of the molecular gas in the fast AGN-driven outflow in the nearby radio-loud Seyfert galaxy IC 5063. Using ALMA observations of a number of tracers (12CO(1-0), 12CO(2-1), 12CO(3-2), 13CO(2-1) and HCO+(4-3)), we map the differences in excitation, density and temperature of the gas. The results show that in the immediate vicinity of the radio jet, a fast outflow, with velocities up to 800 km/s, is occurring of which the gas has high excitation temperatures in the range 30-55 K, demonstrating the direct impact of the jet on the ISM. The relative brightness of the CO lines show that the outflow is optically thin. We estimate the mass of the molecular outflow to be 1.2 x 10^6 Msol and likely to be a factor 2-3 larger. This is similar to that of the outflow of atomic gas, but much larger than that of the ionised outflow, showing that the outflow is dominated by cold gas. The total mass outflow rate we estimate to be ~12 Msol/yr. The mass of the outflow is much smaller than the total gas mass of the ISM of IC 5063. Therefore, although the influence of the radio jet is very significant in the inner regions, globally speaking the impact will be very modest. We use RADEX modelling to explore the physical conditions of the molecular gas in the outflow. Models with the outflowing gas being quite clumpy give the most consistent results and our preferred solutions have kinetic temperatures in the range 20-100 K and densities between 10^5 and 10^6 cm^-3. The resulting pressures are 10^6-10^7.5 K cm^-3, about two orders of magnitude higher than in the outer quiescent disk. The results strongly suggest that the outflow is driven by the radio jet expanding into a clumpy medium, creating a cocoon of gas which is pushed away from the jet axis resulting in a lateral outflow, very similar to what is predicted by numerical simulations.
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