  This paper studies the quintic nonlinear Schr\"odinger equation on
$\mathbb{R}^d$ with randomized initial data below the critical regularity
$H^{\frac{d-1}{2}}$. The main result is a proof of almost sure local
well-posedness given a Wiener Randomization of the data in $H^s$ for $s \in
(\frac{d-2}{2}, \frac{d-1}{2})$. The argument further develops the techniques
introduced in the work of \'A. B\'enyi, T. Oh and O. Pocovnicu on the cubic
problem. The paper concludes with a condition for almost sure global
well-posedness.
