Is it possible to buy tiles in Civilization5 that are more than 3 hexes away from any city?
No, you cannot buy tiles outside the city radius of 3 tiles. You can use a great Artist to culture bomb those tiles or a Great General to build a citadel next to those tiles if you need the strategic/luxury resources there, but don't want to build a city.
The city will continue to expand through culture up to a maximum radius of 5 tiles. But you need a lot of culture for that, the Angkor Wat wonder in that city is very useful for that.
You can never work tiles outside the 3 tiles radius, but you can get the resources on those tiles.