We present an updated study of the planets known to orbit 55 Cancri A using 1 418 high-precision radial velocity observations from four observatories (Lick, Keck, Hobby-Eberly Telescope, Harlan J. Smith Telescope) and transit time/durations for the inner-most planet, 55 Cancri `e' (Winn et al. 2011). We provide the first posterior sample for the masses and orbital parameters based on self-consistent N-body orbital solutions for the 55 Cancri planets, all of which are dynamically stable (for at least 108 yr). We apply a GPU version of Radial velocity Using N-body Differential evolution Markov Chain Monte Carlo (RUN DMC; Nelson, Ford & Payne) to perform a Bayesian analysis of the radial velocity and transit observations. Each of the planets in this remarkable system has unique characteristics. Our investigation of high-cadence radial velocities and priors based on space-based photometry yields an updated mass estimate for planet `e' (8.09 ± 0.26 M⊕), which affects its density (5.51± ^{1.32}_{1.00} g cm-3) and inferred bulk composition. Dynamical stability dictates that the orbital plane of planet `e' must be aligned to within 60° of the orbital plane of the outer planets (which we assume to be coplanar). The mutual interactions between the planets `b' and `c' may develop an apsidal lock about 180°. We find 36-45 per cent of all our model systems librate about the anti-aligned configuration with an amplitude of 51° ± ^{6°}_{10°}. Other cases showed short-term perturbations in the libration of ϖb - ϖc, circulation, and nodding, but we find the planets are not in a 3:1 mean-motion resonance. A revised orbital period and eccentricity for planet `d' pushes it further towards the closest known Jupiter analogue in the exoplanet population.
