I would apply diversity to the makeup air and provide 800 cfm (@200 cfm each), the other 200 can come from the corridor. if all 5 dryers are in function, you can bet any door to the room would be opened often.
With all this makeup air I would bet the sensible loads of the equipment would be negligible, as stated above.
I would only provide cooling to cover any solar/exterior load. For some reason in an old age home I can see people just hanging out there, even if not doing laundry.
If the makeup air is coming directly from the outdoors, i should be cooled.
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