Yes, all HVAC's have that 5 minute delay so that they don't mess up the compressor.....gives it the chance to shut down completely before starting up again.

I'm struggling with my heat pump. In this cold, the aux heat comes on...."the heat strips" that are like the super power because heat pumps use the same unit to AC as to heat.....when it gets really cold then need this extra power like thing that guzzles the electricity......well, I'm noticing that as the temperature is going down down down.....so is the temp in my house. When it was just the normal heating, I sat it at 65 & left it there & it was a constant 70 upstairs.....today as the temp is now -2....I am now sitting at 64 in the room that had been normally 70......the heat pump is running....I have some serious ducting problems that I hadn't taken care of....but it didn't phase it before this afternoon....so I'm thinking there has to be some other problem........like you....I have the upstairs spare bathroom sink dripping to make sure nothing freezes. While dealing with all the cold I have in my house over these last 6 years...I found out that microwaves don't work when the kitchen temp is in the 50's......just another aggravation to deal with. I'm living on a lot of hot tea using my hot pot & have plugged into the bathroom right next to my computer room. Those fingerless gloves are really handy to wear around the house also. You can type & text with them on while still keeping your hands warm