1. He did not like some of them.

2. He disliked some of them.
(Are both the same? Can we use 'some' as in #1?)

3. He couldn't find some of the books.
4. He couldn't find any of the books.
5. He could find none of the books.
(Are they all grammatical? In #3, 'some' is used in a negative sentence. Is this expression grammatical?)

Yes, 1 and 2 mean the same thing.

In #1, you can use "some of them," "any of them," "all of them," and others. In #2, you can use all except "any of them."

#s 3, 4, and 5 are all correct, yes.