You must do 5 different invitational races. It is possible to repeat an event even if your using a different car type and the invitational appears much later in the game than the previous 1. If you have more than 5 and the trophy hasn't popped then just keep at it.
To make sure you're not repeating an invitational simply go onto the invitational screen and click on the event on the bottom right of the screen there's a trophy count if it's empty you haven't done it before.
To check how many you have done already go to career overview. Repeat will be counted here but won't net you the trophy so you could end up with 7 invitationals complete but no trophy if you have mistakenly done the same one a few times.
Feel free to comment any suggestions