It's only 5 days! When I read the title of this thread I thought they were closing your chutes permanently!
Landlords have to maintain and spray the garbage chutes regularly, otherwise they're in violation of city by-laws. It's likely that they were ordered to do this work after a city inspection. Would you rather they just did nothing and then your garbage chute stinks and your apartments become filled with bugs?
I live in a 250 apt highrise, they close the chutes several times a year for maintenance and spraying, and over the Christmas holidays when the building staff are off (they rent a giant dumpster during that time). So far nobody has died from carrying their garbage down the elevators to the dumpsters for a few days. And, we have elderly and disabled people here as well. I'm disabled. My apartment is located behind the garbage chute. If they don't spray it I'm the one who gets an apartment full of ants, spiders, flies (they come out of my washroom vent from the chute) and bedbugs.
For five days tenants can either store their trash on their balcony or get a neighbour or the super to help them take it downstairs to the dumpsters. You should be thankful that they're maintaining your garbage chutes instead of leaving them to become bug infested, broken stink holes. I know of buildings where they locked the chutes permanently after the landlord got sick of cleaning up after pigs that abuse the garbage chutes.