  We prove almost sure global well-posedness of the energy-critical defocusing
quintic nonlinear wave equation on $\mathbb{R}^3$ with random initial data in $
H^s(\mathbb{R}^3) \times H^{s-1}(\mathbb{R}^3)$ for $s > \frac 12$. The main
new ingredient is a uniform probabilistic energy bound for approximating random
solutions.
