A 3 phase motor needs L1, L2 and L3 connections and an earth (4 pins, 4 wires).
It is a balanced load and it doesn't need a neutral.
Even if wired star, the star point should have a net current of zero and doesn't need to be wired to anything outside the motor terminal box.
That's a good thing for 3 phase converters because basic transwave types and modern digital phase converters generally don't provide one.
Potentially a rotary converter could. Doesn't have to, but might.
Some machines need a neutral but this isn't for the 3 phase motor, it's for a worklight or some other funtion of / attached to the machine that wants a 240v supply and it gets this from tapping into one of the phases and neutral.
It might be for a motor starter if that has a 240V coil and needs to use one phase and neutral to operate the contactor and provide piwer to the motor.
But they make starters with 415v coils specifically so that the coil can be powered from two phase wires without needing a neutral, so this isn't an insoluble problem.
Wiring star or delta depends on the motor and the voltage.
Typical dual voltage motor should be wired star on 415v and delta on 240v three phase.
You don't say what voltage your converter outputs or what voltage your motor is made for, but don't take a dual voltage motor like the one above, change it from star to delta and connect to a converter with 415v out. You'll fry it.
I assume we are talking small motors here and not several kW that requires star delta starting.
Motors like that are designed to operate on 415v in delta config. In star config they need 600 odd volts to run. If you connect them star to 415V, this acts as a reduced voltage (and reduced current) soft start. After a couple of seconds and up to speed you crank a big rotary switch that rewires the motor to delta so it is properly matched to the 415v supply and it can make it's rated power.
So the question is why does your machine want 5 pins ? Does it even use them ? What for ? And potentially changing the plug or socket and just leaving out the neutral might be OK. Your new converter might still drive your machine.
But it's on you. If you don't know what you are doing, get help.