  We prove that constant scalar curvature K\"ahler (cscK) manifolds with
transcendental cohomology class are K-semistable, naturally generalising the
situation for polarised manifolds. Relying on a very recent result by R.
Berman, T. Darvas and C. Lu regarding properness of the K-energy, it moreover
follows that cscK manifolds with finite automorphism group are uniformly
K-stable. As a main step of the proof we establish, in the general K\"ahler
setting, a formula relating the (generalised) Donaldson-Futaki invariant to the
asymptotic slope of the K-energy along weak geodesic rays.
