The diffusion constant of TLP5P [J. Chem. Phys. 112, 8910 (2000)], the recently developed five-site rigid nonpolarizable model of liquid water that significantly improves the description of water's density anomaly, has been calculated at a range of temperatures between -25 degreesC and 75 degreesC and pressures between 1 atm and 3000 atm. The diffusion constant, in units of 10(-5) cm(2)/s, for TIP5P water at 25 degreesC and 1 atm is 2.62+/-0.04 as compared with the experimental value of 2.30. This is a significant improvement over most commonly used water models, e.g., for TIP4P and TIP3P [J. Chem. Phys. 79, 926 (1983)] the diffusion constants are 3.29+/-0.05 and 5.06+/-0.09, respectively, and for SPC it is 3.85+/-0.09. The diffusion constant of TIP5P decreases dramatically with decreasing temperature, as is observed experimentally, and the change in the diffusion constant as pressure is increased is also consistent with experimental results.