What is the max distance between top of gutter and the roof tiles?
3-5 centimeters is in the 2-3 inch range.

Any more and you run the risk of water running off the tile and overshooting the gutter.

The gap can vary some because the gutters must slope towards the downspout.

Edit post comments: When you install your new gutters, put the point furthest from the downspout at the highest possible point against the bottom of the roof, and then slope gradually down to your downspout.  You're never going to hit the "maximum" that way.