The fastest way to do this is to use the Drag Strip, but the Drag Strip is locked when you first start the game. So if you haven't unlocked it yet, go play some more and come back when you open it. Go ahead. I'll wait right here for you.
Okay, now that you have that Drag Strip unlocked go start a race session, and select 'PVP'. Don't select the event the game creates for you. This one will be restrictive based on the car you have, you don't want to leave out potential opponents. Slide over and select 'Custom Blueprint'. You want to choose 'Anything Goes', then on the next screen select 'Showdown'. Finally select 'Create Blueprint' and you are ready to race.
Race 5 times and the achievement will pop. After you create the race, there is no reason to recreate it over and over again, you can go to 'Custom Events' the next time you race and you will see it already created for you.
I finished this and the 5 PVP races achievement in about 30 minutes on June 30, 2020 (years after release) so it's still possible to get it without a lot of trouble. (Don't forget to race once in an X class car and once in D class car to get Tortoise and the Hare along the way)