The theft at the center of Fast Five is, essentially, a massive amount of cash. Crime lord Herman Reyes is in league with the police in Rio de Janeiro, and has stashed $90 million in the police vault. Although stealing the money from the vault initially seems impossible, Dom's crew eventually decides to raid the building and physically remove the vault from the police station.
Then, the movie transforms into an extended car chase as Dom and Brian (Paul Walker) drag the vault with their cars. Eventually, the two of them are cornered and Dom tells Brian to go on without him. Dom then proceeds to drive his car into the police and Reyes' forces, which have both been in pursuit. Dom uses the vault to destroy their vehicles, but is eventually cornered by Hobbs (Dwayne Johnson), an American agent who has been pursuing Dom's crew throughout their time in Rio.
Brian returns to save Dom, and Hobbs executes Reyes. Hobbs then agrees to give Dom and his crew a 24-hour head start, provided that they leave the safe behind. They agree, and drive off into the sunset.
It isn't until after they've gotten away that Hobbs opens the safe and finds it empty. During the chase, Dom's crew switched safes, allowing them to get out with the $90 million.