What are the correlation between the Big 5 (OCEAN) dimensions of personality?
My answer to the question on evidence for the GFP provides numerous references on the correlations between the Big 5:

What is the support for a global personality factor?

The key bit of the answer is as follows:


  van der Linden et al 2010 extend the work of Musek (2007) by presenting a meta-analysis of Big 5 intercorrelation matrices
   in order to assess the evidence for a General Factor of Personality.
  Table 2 shows the meta-analytic average scale intercorrelations for the big 5 measures included in the meta-analysis. It shows how across a wide range of measures and measurement procedures, the Big 5 scales moderately intercorrelate. The average absolute unadjusted correlations between the Big Five was 0.23. 




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 &amp; 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, &amp; 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 &amp; 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.

References


Anglim, J., &amp; O'Connor, P. (2018). Measurement and Research Using the Big Five, HEXACO,
and Narrow Traits: A Primer for Researchers and Practitioners. Australian Journal of Psychology. https://psyarxiv.com/a78g2/download
van der Linden, D., te Nijenhuis, J., &amp; 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.