Slow earthquakes, like regular earthquakes, result from unstable frictional slip. They produce little slip and can therefore repeat frequently. We assess their predictability using the slip history of the Cascadia subduction between 2007 and 2017 during which slow earthquakes have repeatedly ruptured multiple segments. We characterize the system dynamics using embedding theory and extreme value theory. The analysis reveals a low-dimensional (<5) non-linear chaotic system rather than a stochastic system. We calculate properties of the underlying strange attractor like its correlation and instantaneous dimension, instantaneous persistence, and metric entropy. We infer that the system has a predictability horizon of the order of days-weeks. For the better resolved segments, the onset of large slow slip events can be correctly forecasted by high values of the instantaneous dimension. Longer-term deterministic prediction seems intrinsically impossible. Regular earthquakes might similarly be predictable but with a limited predictable horizon of the order of their durations.