measurement - What are the correlation between the Big 5 (OCEAN) dimensions of personality? - Psychology & Neuroscience Stack Exchange
My answer to the question on evidence for the GFP provides numerous references on the correlations between the Big 5:
The key bit of the answer is as follows:
You can also check out other work discussing higher-order factors (typically one or two factor models). These imply a correlation between the Big 5.
To quote my own primer on the Big 5 (Anglim & O'Connor, 2018: https://psyarxiv.com/a78g2/download):
Researchers have posited one and two factor higher-order models of personality suggesting that the Big Five may not be the broadest meaningful level of personality analysis (Anusic, Schimmack, Pinkus, & Lockwood, 2009; Digman, 1997; Musek, 2007; Veselka et al., 2009). Notably, a single, broad factor (termed the General Factor of Personality; GFP) has been proposed to account for meaningful trait variance at the highest level (e.g., Musek, 2007), although see various critical perspectives (Davies et al., 2015; De Vries, 2011; Revelle & Wilt, 2013) .
Thus, you could check out those references for further background on one and two-factor models. Such papers will generally also discuss the structure of correlations between the Big 5 and arguments for and against why they are meaningful.
van der Linden, D., te Nijenhuis, J., & Bakker, A. B. (2010). The general factor of personality: A meta-analysis of Big Five intercorrelations and a criterion-related validity study. Journal of Research in Personality, 44(3), 315-327.