Direct coexistence simulations between the fluid and solid phases are performed for several ices. For ices Ih and VII it has already been shown that the methodology is successful and the melting point is in agreement with that obtained from free energy calculations. In this work the methodology is applied to ices II, III, V, and VI. The lengths of the direct coexistence runs for the high pressure polymorphs are not too long and last less than 20 ns for all ices except for ice II where longer runs (of about 150 ns) are needed. For ices II, V, and VI the results obtained are completely consistent with those obtained from free energy calculations. However, for ice III it is found that the melting point from direct coexistence simulations is higher than that obtained from free energy calculations, the difference being greater than the statistical error. Since ice III presents partial proton orientational disorder, the departure is attributed to differences in the partial proton order in the water model with respect to that found in the experiment. The phase diagram of the TIP4P/2005 model is recalculated using the melting points obtained from direct coexistence simulations. The new phase diagram is similar to the previous one except for the coexistence lines where ice III is involved. The range of stability of ice III on the p-T plot of the phase diagram increases significantly. It is seen that the model qualitatively describes the phase diagram of water. In this work it is shown that the complete phase diagram of water including ices Ih, II, III, V, VI, VII, and the fluid phase can be obtained from direct coexistence simulations without the need of free energy calculations.