It depends on other parameters as well. If your corals are already struggling in the tank due to other parameters, a little bit of temp fluctuation will push it over the edge.
It's very easy to keep the temps stable in the winter time. It's easier to heat water than to cool it. In the winter time, you should be able to control a much tighter fluctuation. For most, it should be within the hysteresis of the controller. In the summer time, it's a total different story. And the amount of temp spike your corals can handle will depend on other parameters as well.
For my tank, winter time +/-0.2degrees. For summer time, +2degrees during the halides period. On a really hot day and if I forgot to turn on the AC, the temps will hit the max +3 degrees in which case the halides will turn off.
If you run your tank normally at 76, a +5 degrees might not be that bad. If you run your tank at 80degrees, a +4 degrees can do some damage. I personally wouldn't look at the absolute change in other people's system. I would keep the tank at the temperature I'm comfortable of keeping it stable and have the +/- window as small as possible.