I created a new document with 3mm bleed and 5mm slug, portrait, facing pages checked, 120mm x 160mm. But bleed & slug lines are outside the page!
Why is that?
Bleed and slugs are meant to be cut off after printing. Therefore you don't want them on the page.
By being outside the InDesign page definition, it should make it clear that when printed, only the actual page will be seen. When you export to a press-ready PDF or output the InDesign file with printer's marks, the additional areas for bleed and slug are included. The output file is increased in width and height to allow these areas to show in the press-ready documents so that pre-press departments, pressmen, and bindery personnel (the people that cut the final piece) can see them. These are the only people that need to see the bleed and slug.
You can see this yourself if needed. Create a page with a bleed and slug and then place items on the page which extend into these areas (off the page). Then export the file to PDF/X-1a with marks and view that resulting PDF.
Bleeds are used to ensure any trimming which may be slightly inaccurate does not result in the actual stock showing at the edge of the piece. Slugs are only used to pass along production notes and are never intended to be part of any actually printed piece a reader would see.