If you're taking the ASWB exam before 1/1/2015, it's the DSM-IV-TR you have to know. After that, DSM-5 steps up. (People scheduling the exam toward the end of 2014 may want to delay a little bit so as not to be learning about an outdated book.)
What you need to know about the DSM for the social work licensing exam is free on the web. Here are a couple of places to look: