The Five-Factor Model (FFM) describes five independent elements of personality (see table below) that are present in all individuals to varying degrees (Blandin, 2013; Boyle, 2008; Cooper et al., 2012).
However, the relationship between personality, communication, and team performance is not straightforward.
Traits are not just 'good' or 'bad'. For example, aspects of personality that we might consider to be positive, such as Agreeableness, do not automatically ensure effective communication and effective teamwork.
The FFM is generally well-regarded by psychologists and has been applied to clinical practice (Blandin, 2013; Lloyd, 2015; Macht & Nemard, 2015). It has also been used to study team performance with varying results:
One study (Macht & Nembard, 2015) looked at the way Agreeableness influenced team communication and overall team performance. No link was found.
The same study found that Neuroticism, which is usually viewed as an undesirable factor, has been found to be positively related to team performance: "a team that is more temperamental on average will communicate more, ultimately leading to better performance" (Macht & Nembard, 2015).
A team's performance benefits from having members who have wide ranging scores on both Extraversion and Introversion (Lloyd, 2015; French & Kottke, 2013). Too many extroverts within a team may lead to increased role conflict and social distractions because extroverts are more likely to dominate and be more active than others in social settings (French & Kottke, 2013).
There are many versions of the FFM (sometimes called The Big Five, or CANOE) on the web but there is no official website, I encourage you to Google the FFM and take the test if you are interested.