why 3 phase why not 4 or 5 phase

Going from 1 phase to 3 phase gives efficient improvement by 50% increase (which can be utilized toward reduced copper by 75%). Increasing the number of phases arbitrary more than that (infinite) can only increase efficiency very little (something of the order of 7%). This is efficiency comparison only. In any case, using 3 phase, you can get 3 times the power of the single phase (if you generate same voltage and current in any one phase as that of a 1 phase generator) and so on.br /Also analyzing for higher phases, in multiples of 3 i.e. 6,12 or higher lines, power transfer curve would be dropping e.g. 6 phases would add twice power than three phases but 12 phases do not add power double than that of 6 phases. Also higher phases would cause more constrain at grid.