I have looked at the big 5 personality traits, and they include 5 basic factors: openness, extraversion, conscientiousness, neuroticism, and agreeableness. Why is empathy not on the list?
The basic goal of research on the big 5 is to identify those dimensions of personality that can account for the most important differences between people.
How do you determine what is important and "makes the list"? The research from which the Big Five have been derived relies on the lexical hypothesis. In a nutshell, the idea is that if a trait is important, it should be part of our language. So personality researchers such as Allport and Cattell have devised long lists of words existing in our lexicon used to describe the traits of people. Then they asked people to judge themselves with regard to these traits. Finally, they tried to identify underlying (common) dimensions in these trait descriptions by using statistical analyses (e.g. factor analyses). For example, if someone agrees to being a "friendly" person, he or she will probably also agree to being a person who "cares about people". These analyses resulted in the 5 very broad dimensions of personality.
What about empathy? Empathy is highly related to agreeableness. In fact, if you look at personality questionnaires, the agreeableness scales are likely to tap into empathy:
- For example, the NEO agreeableness subscale of the International Personality Item Pool includes items such as: "[I] Am concerned about others." or "[I] Sympathize with others' feelings." which are essentially items measuring empathic concern.
- The NEO-PI-R (Costa & Macrae, 1992) is one of the most widely used Big Five questionnaires (with 240 items it's a pretty large and comprehensive one). It describes agreeableness as "the kinds of interactions an individual prefers from compassion to tough mindedness." It has two sub-scales that are related to empathy: Altruism ("active concern for the welfare of others") and Tender-Mindedness ("attitude of sympathy for others.").
This makes clear that from the perspective of the Big Five, empathy may be regarded as an element of agreeableness.
All of the above should not imply that it has no value to think about and measure empathy as a specific trait (rather than the general agreeableness factor). This is just about different research goals. The goal of the Big 5 is to be maximally parsimonious. Some detail will be lost by this strategy. However, if you are specifically interested in empathy, it may make more sense to focus on it at the cost of parsimony.