A flat Friedman-Roberson-Walker universe dominated by a cosmological constant (Λ) and cold dark matter (CDM) has been the working model preferred by cosmologists since the discovery of cosmic acceleration. However, tensions of various degrees of significance are known to be present among existing datasets within the ΛCDM framework. In particular, the Lyman-α forest measurement of the Baryon Acoustic Oscillations (BAO) by the Baryon Oscillation Spectroscopic Survey (BOSS) prefers a smaller value of the matter density fraction ΩM compared to the value preferred by cosmic microwave background (CMB). Also, the recently measured value of the Hubble constant, H0=73.24±1.74 km s−1 Mpc−1, is 3.4σ higher than 66.93±0.62 km s−1 Mpc−1 inferred from the Planck CMB data. In this work, we investigate if these tensions can be interpreted as evidence for a non-constant dynamical dark energy (DE). Using the Kullback-Leibler (KL) divergence to quantify the tension between datasets, we find that the tensions are relieved by an evolving DE, with the dynamical DE model preferred at a 3.5σ significance level based on the improvement in the fit alone. While, at present, the Bayesian evidence for the dynamical DE is insufficient to favour it over ΛCDM, we show that, if the current best fit DE happened to be the true model, it would be decisively detected by the upcoming DESI survey.