We study the TIP5P water model proposed by Mahoney and Jorgensen, which is closer to real water than previously-proposed classical pairwise additive potentials. We simulate the model in a wide range of deeply supercooled states and find (i) the existence of a non-monotonic ``nose-shaped'' temperature of maximum density line and a non-reentrant spinodal, (ii) the presence of a low temperature phase transition, (iii) the free evolution of bulk water to ice, and (iv) the time-temperature-transformation curves at different densities. ; Comment: RevTeX4, 4 pages, 4 eps figures