1. She thinks reading books.

2. She thinks of reading books.
3. She thinks about reading books.
4. She thinks that she is reading books.
5. She thinks to be reading books.

(Are they all grammatical?)

2, 3, and 4 are fine. 3 and 4 are the best.

1 and 5 are not correct.

Out of the five sentences you provided, only the first three are grammatically correct:

1. She thinks reading books. [Correct]
2. She thinks of reading books. [Correct]
3. She thinks about reading books. [Correct]

These sentences are all expressing the same idea that she is thinking about the act of reading books. However, they differ slightly in their structure and usage.

1. "She thinks reading books."

This sentence is an example of a gerund phrase, where "reading books" functions as a noun. The verb "thinks" is followed by the gerund "reading," which acts as the direct object of the verb.

2. "She thinks of reading books."

In this sentence, "of reading books" functions as a prepositional phrase, and it indicates what she is thinking about. The verb "thinks" is followed by the preposition "of," which is then followed by the noun phrase "reading books."

3. "She thinks about reading books."

Similarly to the previous sentence, "about reading books" functions as a prepositional phrase that indicates what she is thinking about. The verb "thinks" is followed by the preposition "about," which is then followed by the noun phrase "reading books."

As for the other two sentences:

4. "She thinks that she is reading books." [Incorrect]

This sentence is grammatically incorrect because it repeats the subject pronoun "she" while also using the pronoun "that" as a subordinating conjunction. To correct the sentence, you can remove either the second "she" or the subordinating conjunction "that."

5. "She thinks to be reading books." [Incorrect]

This sentence is grammatically incorrect because it uses the infinitive "to be reading" as an object of the verb "thinks." Instead, you can use one of the correct versions mentioned earlier, such as "She thinks of reading books" or "She thinks about reading books."