CPA security for block ciphers?
The book introduces two concepts, and warns not to confuse them with each other:


Encryption schemes: Which can have varying key lengths; and
Block ciphers: Which have fixed-length black and key lengths.


Chapter 3 of the book mainly speaks about encryption schemes. For instance, take a look at the proof of CPA-security of the CTR mode (Theorem 3.29, and Figure 3.8): The permutation $F_k$ used at the heart of the CTR construct can have varying key lengths.

However, chapter 5 mainly discusses block ciphers. These are practical constructs based on the theoretical ideas of encryption schemes (as the chapter title implies). The security of block ciphers (DES, AES, etc.) cannot be formally proved (at least at the present), since there exists no notion of concrete security, in contrast to asymptotic security. 

That said, there has been some attempts at defining security notions for concrete security as well. Rogaway, for instance, has written a nice paper on defining security for "ordinary" hash functions (in contrast to "families" of hash functions).

A related question on CSTheory is Hardness Guarantees for AES, where the OP asked about provable measures for the AES block cipher.