We provide a closed-form expression for the motivic Kontsevich-Soibelman invariant for M-theory in the background of the toric Calabi-Yau threefold K_{\mathbb{F}_0}. This encodes the refined BPS spectrum of SU(2) 5d {\cal N}=1 Yang-Mills theory on S^1\times \mathbb{R}^4, corresponding to rank-zero Donaldson-Thomas invariants for K_{\mathbb{F}_0}, anywhere on the Coulomb branch.
