How to make an vertex on crossing edges?

[micheus]

I need some vertex's on exact points on a cylinder (like: on x5, z10 and x5 z40) and made this cube as a reference. But i can't find an option to make a vertex exact there.

lennart, by reading this sentence I suggested you to use Absolute Command->Move [LMB] which will allow you to enter the three coordinates for the point/vertex as you had exemplified.
If these vertex in a specific location will move the cylinder or modify it's geometry that will be defined in Absolute command if you check the Move object option.

In the image, it's not clear if the two objects are in contact each other or not, and also we are seeing the viewport in perspective which mean the long selected edge on the "box" is far away from the short one on the "cylinder" - so, I believe they are not in contact.
Then, for this situation it looks like you want to create and align the vertex by using the camera projection - we don't have an option for that, but you could to approximate its location by selecting the edge you want to add the vertex and by using the Cut command [RMB] and sliding the new vertex along the edge util it match with the desired location (visually, of course).

But, if the objects are contacting each other, then the approach shown by ivla should work.

Eventually you would need give us more information, share the source file and/or show a sample of what you trying to achieve (a reference image, maybe).