Is there a height limit?

The question is simle really, is there a height limit in GTA5? A limit to how high a player can go? Whether it is using a cheat, a helicopter or a plane?

There is a height limit in GTA 5 as well, yes.

Previously, the one in GTA 5 is 12800 ft, which is around 4000m respectively.
Old wiki page

This wiki page has been updated on December 2014 to change these limits. It's now indicate that the limit is 8100 ft (2470m), which coincide with Bens' answer.
Actual wiki page

Cheers.

I flew one of the big planes to the ceiling, if you put it in first person point of view it shows on the altimeter (aircraft instrument) that the maximum height is 8,100 ft before it forces you down to 8,000 ft.