If you book an airport transfer with any limo service (NCC or Noleggio con Conducente) the price for 5 or 6 adults in a minivan should be 70€ to no more than 90€,
Just Google Airport transfers Rome (or NCC Rome) and check the best deals.
Regarding the taxi they were protesting with the City earlier this year and threatening to end the flat fare of €50 because of the incredible amount of road work currently in Rome which makes it impossible to cover the distance in reasonable time. I don’t know if the flat rate has ended, in any case you can’t fit 5 people in a regular car, you’d need a minivan and even at 50€ per taxi, if you use two, it will be more than a minivan with a limo service.