I find that the S3 focuses as close as about 9cm from the subject regardless of whether macro is toggled on or off. If this is so then it suggests to me that the macro facility acts as any other scene mode where the software simply manipulates the settings to accommodate the scene. It doesn't allow you to get any closer.
The S5 has no macro mode yet focuses to a similar proximity to the subject as the S3 (about 9cm). My experience is that you will be more likely to achieve this if you start by trying to focus from further away and steadily move closer, touching the screen as you go. For some reading, going very close in then steadily moving out doesn't seem to work so well resulting in the red focusing rectangle turning to green further away that 9cm!
The S5 has no macro mode yet focuses to a similar proximity to the subject as the S3 (about 9cm). My experience is that you will be more likely to achieve this if you start by trying to focus from further away and steadily move closer, touching the screen as you go. For some reading, going very close in then steadily moving out doesn't seem to work so well resulting in the red focusing rectangle turning to green further away that 9cm!