The maximum power that the unit uses is 1.20kW for cooling and 1.47kW for heating, although Assuming that your unit is a modern "inverter" style then the power consumption will be reduced if less cooling/heating is required. Even if it isn't an inverter then the compressor still cycles on/off to maintain the set temperature.
For simplicity, let's say you set the thermostat as low as it can go and the unit runs non-stop for an hour; your unit will consume 1.20kWh of electricity (1.47kWh if it was heating) - The price of a kWh will be on your electricity bill; depending on your tariff, time of day may also affect the price.
The output of your solar system will depend on where in Australia you are located, its orientation, roof angle and any shading, but 3-4kWh per kW is a reasonable figure to achieve, so a 5kW system should output at least 15Kwh per day. Over 7 hours this works out at a little more than 2kWh per hour, which would cover the operation of your AC. You can get a better idea of your proposed system's output using an online calculator such as this one
The "capacity" figures refer to the heating and cooling capacity of the system.
Air conditioners are actually a "heat pump" they move heat from inside to outside (cooling) or outside to inside (heating). Heat pumps can move more heat than the energy they consume. The ratio of energy moved to energy consumed is the EER or coefficient of performance (COP) - You will see this value quoted on the spec sheet of any system.
From EnergyRating.gov.au
How can the capacity output of an air conditioner be greater than the
power input?
For air conditioners, the measure of energy efficiency is
the Energy Efficiency Ratio (EER) for cooling and the Coefficient of
Performance (COP) for heating. The EER and COP are defined as the
capacity output divided by the power input. This is achieved by the
use of a refrigeration heat pump which collects internal heat and
moves it outside when in cooling mode, or collects ambient heat from
outside and moves it inside when in heating mode. The apparent
efficiency of heat pumps is high as they can move much more low grade
energy in the form of heat than the electrical energy they require.
As a result, despite their reputation for being energy hogs, air conditioning units are much more efficient than other forms of electric heating. A 1kW bar heater (or fan heater) will use 1kW of electricity to produce 1kW of heat while your AC unit gives you 3.74kW of heat for the same 1kW of electricity in.
