How do you determine which tile belongs to which city. Switching tile ownership.

[Malus]

How do you determine which tile belongs to what city? and is it possible for tiles to switch "city ownerships" and if yes how do i do it.

I need to make a peacedeal with another player and i need to give him few cities but i would like to keep certain tiles that should be in 5 tiles range from another city

[ForevaNoob Wonemorturn]

Open the city management (x2 click on the city name), go top right side of it, and organize it at will. On the inner city view, you'd be able to tell which tile is worked by who, in case there is another city involved. There, switching at will between the two cities managements, click on a tile to decide which city is gonna rule it and what to do with any of those tiles within the "3 tiles radius" of each city, circles that could sometimes penetrate themselves.
Click and rule, the Civilization law.
Click everywhere to rule anywhere being mine.
I believe if you first take control of the tile, as I described already well enough I hope, i you give the next town, you might keeping the use of that tile, but I'm not sure how the tile exchange will work precisely. But take control, meaning work the tile and try for yourself.
Last thing, there is nothing like a "5 tiles range" rule.
The workable tiles are all and only the ones within a 3 tiles radius. Your city will expand slowly but goody along the game, feeling the gap, sometimes up to 6 or 7? tiles away to claim every available luxury or resource around which is still free for the taking. If that tile has been "historically taken" by that city, it should belong to that particular city for ever, that's my guess.
You won't be "working" that tile but, with the proper improvment built on it, benefit of its gift. Make peace and see.
Save, try, and reload, my first Civilization 5 teacher. And the only teacher always available...

[Malus]

i never had a city expand beyond 5 hexes even if it had enghout culture, thats why i thought its the max range
switching which city works that tile unfortunatly does not change which city owns the tile

[ForevaNoob Wonemorturn]

Not when the city owns the tile already. I was hopping maybe before giving the city away.
I'm pretty sure about 6 tiles away. And 50% only for 7.
If there is no one around, 'seems quite possible.