Underground cable outside for electric courtyard gate: 3x1.5mm² or 5x1.5mm²?

Most motors do not even have a separate control line, and more than 3.5 kW for the gate drive seems highly questionable. It will surely become clear quickly if you ask the installer to provide you with the technical documents. Have you planned an integration into your home control system? If so, wouldn’t the plans have already been of interest?

Most motors don’t even have a separate control line, and more than 3.5kw for the gate drive seems highly questionable.

But the control unit next to it possibly does

Just googled a bit, for example skimmed through a document from Hörmann. They say it should be 3x1.5mm for the motor and for example (!) 6x1.5 control lines for push buttons of all kinds.
So if there should be a switch in the house, then this drive would need corresponding control lines that lead from the house there. Maybe something can also be bridged via radio.

We have a summer drive, due to lack of a button or other external contacts it works with 3 wires. With a button and feedback, 5 wires are still not enough.

I don't really know much about gates, but if it works roughly like my awning drive, then 2 wires are needed to control the up/down/close function. The phase comes via a switch either to the up or down wire, plus N and PE. That means you need 4x1.5. Since this is not available as a standard cable, the manufacturer probably says 5x1.5. This has nothing to do with the motor's power. Get the wiring diagram for the connection. If it is like this, you can place the switch at the gate and then operate it there with a key and/or by radio. Then 3x1.5 from the house is enough. It only gets complicated if the switch has to be placed inside the house.

Or does the motor need three-phase current?

So our yard gate operates with 1 phase, and the control lines for switches branch off separately from the motor (probably low voltage). The manufacturer is Tousek.