Yes its not unusual to take 5 minutes to get useful cabin heat when starting a car from cold.
On cars with an internal combustion engine (petrol or diesel) the engine is kept cool by circulating coolant (a mixture of water and antifreeze) around the engine and then cooling it by passing it through a radiator at the front of the car. Engines work best when hot - with the coolant at around boiling point. (Its best drive more gently until the engine has reached its operating temperature. There is normally a blue light telling you the engine is cold. Take it easy until this light goes out) ) If the air passing through the cooling radiator is cold it can take longer to warm up. There is normally a thermostat in the system that stops the coolant circulating until the engine is warm , so it heats up quicker.
For cabin heating there is a second small radiator behind the dashboard. When you switch on heating a valve is opened so some of the engine coolant passes through this heater radiator and it gets hot.When you adjust the heating level it adjusts the rate of flow of hot coolant (which may not yet be hot

)
Air is directed to the cabin and heats up as it passes through this little hot radiator. Some comes in as you drive along, or you can boost the amount of air by using the fan. You can also distribute the hot air where you need it most , such as to a frosty windscreen , or your feet or a bit of both. You may need to adjust air flow , fan speed etc to suit your needs and comfort as the car warms up.
A car with climate control can adjust heating and air distribution automatically using electronics . Or you can set things manually. Your system can also control and cool temperature automatically (or manually) by using air conditioning.
Put in very simple terms Airconditioning uses a second separate system of radiators to cool air below the ambient air temperature.
There is quite a bit to learn to have full control of heating and cooling. Its probably in the drivers handbook which you can download free from Honda as a pdf
https://www.honda.co.uk/content/dam/local/uk/cars/owners/manuals/2018%20Jazz%20Owners%20Manual.pdf