5. C.

The scenario with the fewest math books $(S)$ occurs when the number of physics books (W) is at its maximum, as shown below:

Three math books SSS can also appear in other positions simultaneously, as indicated by the arrangements showing (1), (2), and (4) are correct; statement (3) does not hold in the following arrangement:
SSWSSWSS ...WSS.
5. There are 53 books of mathematics and physics on the bookshelf, where no two physics books are placed next to each other, but every mathematics book is adjacent to another mathematics book. Given the following four statements:
(1) There are at least 35 mathematics books;
(2) There are at most 18 physics books;
(3) There are 3 mathematics books placed consecutively;
(4) In 12 consecutive books, there are at least 8 mathematics books.
Among them, the correct statements are ( ) in number.