As we all know each city that is just founded has a 1 tile border space (not the working tiles the borders). Is there a way to change the starting space tiles from one to 5?

Not directly, but you could assign a quick-build, high culture-producing improvement that can accomplish this. What are you trying to accomplish?

I want to make a city have bigger borders when is founded. I want to eliminate improvements and wonders that generate culture. Its unsutisfying when a new founded city has only its original borders and the iron is 3 tiles away. So I want to enlarge its borders.

Actually there may be a way to do that on the general settings page. If you set the cultural level factor to 0, all cities should start out with max culture area (I think- I'm not at home so I can't try it) But then it will never expand.

You can't set it to 0 I have tryed.

Well, I tried changing that 'border factor' but it crashed the game IIRC.
The game wouldn't load anymore.

Perhaps I put in too big a number :D

As for the question at hand, I don't think it's possible, Sourboy's solution is the best you can get AFAIK :)
And put that border factor to one perhaps.
you can even make sure the improvement gets build by having a few other improvements require it.

Maybe if you set it to 1 it would work- apparently the number is raised to the n power for each level, so as soon as you get 1 culture point you should reach the highest level (1^n=1). But that very well may cause a game crash. If it doesn't work, try 2, your borders will still expand fully at 32.

I know that but I have to build an improvement first. I don't want to build an improvment or any building, I just want to change the starting borders per city. I guess thats not possible.