This is a non dwelling unit. I assume all the appliances may be in use at the same time. Since 120/208 is available I assumed installing a sub panel to the laundry area using three phase would be appropriate?
It will help with load balancing on the service/upstream feeders at the very least as compared to only running two phases to this area.
If you figure 30 amps for dryers and 10 amps for the washers you should have plenty of capacity as I would be willing to bet the dryers don't draw much more than 23 amps if connected to 240 volts, and probably would reduce to about 20 amps @ 208 volts. The washers may draw up to 10 amps, but probably only during the spin cycle, the rest time it may be significantly less.
Next step is realizing that if you have 30 amps of load between each phase, the actual phase currents are 1.73 times each individual load current so if you only had three 30 amp loads equally balanced you would have 52 amps of current on each phase.
Now consider if the load really is 20 amps as suggested it may be that drops to only 35 amps. That is just for three dryers, you still need to add the other two - 20 (or 30) amps for two phases and 35 (or 52) to the phase that is common to both of the unbalanced portion of the load, plus your washers need added yet, which will be 10 amps per unit to each phase they are connected to.
I come up with best balance (assuming all are fully loaded at one time and loads of 10 and 30 amps as mentioned in OP) being three dryers balanced across all phases, put the remaining two from (for example) a to b and b to c , at this point you will have phase loads of 82, 104, 82. Then put two washers on each of the 82 amp phases to get the balance to 102, 104, 102. Put the remaining washer on any phase you wish.
