In round figures, your motor takes 10A at 230V, in normal running.
When an induction motor is started "direct on line" (as in by a switch or contractor rather than an electronic speed control) it can take anything from three to six times more current than its running value.
Whatever you use to switch power to the motor needs to allow for that.
This is the typical setup used to switch power to such a motor:
A fuseholder plus AM rated fuses (or an equivalent motor circuit breaker)
A contactor:
An overload detector:
**broken link removed**
The contactor is the part than needs controlling to switch the motor on and off. Depending on the type you choose, that may need anything from 24V through 110 or 115V, or more.
You have to provide that control voltage and switch it from your electronics device; using a 5V supply for the electronics and a small SSR is likely the simplest way of switching the voltage to the contactor.
Nothing anyone else has said has been particularly wrong, they have just been trying to find out what exists and what else is needed.
Without knowing exactly what control gear (if any) is supplied with the machine that has the motor in it, as you have not answered that question, all I can assume is you need all of it.
This is a section of a control cabinet we built for an industrial machine.
You can see the same basic setup as with the parts I linked above, repeated a number of times (plus other contactors for controlling reversing motors or other things).