In the Fast Five ending, the crew drags the vault through Rio behind two cars, swaps its contents with a trash truck, and Luke Hobbs opens an empty vault while Dominic Toretto (Dom) and Brian O'Conner get away with the money. In other words, the crew escapes with the money, not the vault itself.
The trick works in steps. First, the vault is the only thing the authorities can see, so the chase locks onto it: two cars tow it through the streets of Rio, and everyone pursuing the crew follows the moving steel box. Second, the crew trades the vault's contents with a trash truck, so the cash leaves the chase while the box keeps rolling. Third, the vault is opened in front of Hobbs and turns out to be empty. In my opinion, that swap is the cleverest piece of misdirection in the saga, because everyone chasing the vault is chasing the wrong object.
The production context explains why the set piece looks the way it does. Brazilian press reported that the Rio-set scenes were filmed in Puerto Rico, with the production then moving on to Atlanta, Georgia, and Primera Hora reported that about 60 specially built cars were brought to the island for the shoot. Rio de Janeiro itself supplied aerial and location shots, so the streets the vault crosses are mostly Puerto Rico playing Brazil.
The human side of the ending is just as deliberate. Hobbs kills the crime boss Hernan Reyes, which removes the villain, and Hobbs then lets Dom and Brian go with a head start rather than arrest them. Everyone ends up wealthy and free. Brian and Mia leave Rio expecting a child, which pays off the pregnancy revealed earlier in the film.
Compared with the rest of the series, the finale shifts the weight of the saga. The earlier films in release order, such as Fast & Furious (2009), center on crews and street racing, while this one ends on a heist that depends on a plan rather than a race. The closing beach race is a small nod back to that starting point. It could be argued that this is where the series becomes a heist saga. The timeline adds a detail: Fast Five is fourth in chronological order, Fast & Furious 6 is fifth and Tokyo Drift is sixth, which is why Han is still alive here. The mid credits scene then points forward by showing that Letty may be alive. For where the story goes next, see Fast & Furious 6.