To access Future Funland, the fifth world, you must place first in all of the Trophy Races and acquire the Wizpig Amulet. You don't need the TT amulet to access the fifth world, but once you're in Future Funland, you'll need it to race Wizpig again.
Drive to the Trophy sign (near the Lighthouse) and park in front in of it to gain access. You will see your character enter into the lighthouse, which then turns into a rocketship and blasts off to space.