I prefer to buffer the P.P. using for e.g. a 2N7000 transistor, the output or drain of this FET would go to the SSR and no resistor needed, the PC 5v could still be used.
This system will not be able to control the RPM, due to the SSR being a switch (on/off).
And a 1 ph induction motor is unsuitable to be used with speed control.