The ability of simple potential functions to reproduce accurately the density of liquid water from -37 to 100 degrees C at 1 to 10 000 atm has been further explored. The result is the five-site TIP5P model, which yields significantly improved results; the average error in the density over the 100 degrees temperature range from -37.5 to 62.5 degrees C at 1 atm is only 0.006 g cm(-3). Classical Monte Carlo statistical mechanics calculations have been performed to optimize the parameters, especially the position of the negative charges along the lone-pair directions. Initial calculations with 216 molecules in the NPT ensemble at 1 atm focused on finding a model that reproduced the shape of the liquid density curve as a function of temperature. Calculations performed for 512 molecules with the final TIP5P model demonstrate that the density maximum near 4 degrees C at 1 atm is reproduced, while high-quality structural and thermodynamic results are maintained. Attainment of high precision for the low-temperature runs required sampling for more than 1 billion Monte Carlo configurations. In addition, the dielectric constant was computed from the response to an applied electric field; the result is 81.5 +/-1.5 at 25 degrees C and the experimental curve is mirrored from 0-100 degrees C at 1 atm. The TIP5P model is also found to perform well as a function of pressure; the density of liquid water at 25 degrees C is reproduced with an average error of similar to 2% over the range from 1 to 10 000 atm, and the shift of the temperature of maximum density to lower temperature with increasing pressure is also obtained.