Why if my air conditioner dial is set to 80, the air unit will not shut off until 75 degrees?

I live in an apt complex and it is an older thermometer for the central air. I have the unit set on Auto and on Cool, I slide the desired temperature to 80 degrees (and when the temperature reaches this it turns on the air unit) which will not shut off until 75 degrees, which can take a couple of hours? This does not seem right, I was under the impression that an air unit cools until the desired temperature of 80 is reached. Why is it going 5 degrees lower before shutting off, and why is it taking so long to turn off? Should I have it checked out, or do something different? Thank you.