That's odd, but maybe it's just sloppy timekeeping instead of a plan. Public clocks get ignored for maintenance all the time, they just run fast or slow. You can check them against your phone, which gets the time from satellites. Honestly, who would bother to change that many clocks... seems like a lot of work for no real reason.
The clock outside our post office has been ten minutes fast for three years now! Everyone just ignores it and checks their phones instead. I asked about it once, and they said the repair cost wasn't in the budget. So yeah, it's definitely more about maintenance laziness than some big plan!
charlie373 said it's a lot of work for no reason, but that's exactly why it's suspicious. If it was just broken, they'd all be wrong in different ways. Five clocks all exactly five minutes fast? That's not an accident, that's a setting. Maybe the city council or a business group did it to make people think they're late, so they hurry up and spend more money. It's a cheap trick to boost productivity or sales without anyone noticing.