In this model (a good one, BTW!) parent_id is not telling you what tree level the category is at, but is a reference to it's parent category.
Let's look at your example:
table category
id title parent_id
1 antiques 0
2 art 1
3 books 0
4 property 0
5 detached 1
Your main categories are antiques, books, and property, since they have a parent_id of 0 (i.e., no parent).
The subcategories art and detached have a parent_id of 1, which references back to the category with the id of 1, antiques.
The layout is something like this:
antiques
art
detached
books
property
If you add some more rows to the table, say:
id title parent_id
6 old 2
7 older 2
8 hotels 3
9 houses 3
10 oldest 2
Then you wold have a structure like this:
antiques
art
detached
books
old
older
oldest
property
houses
hotels
HTH