I have 6 recessed lights in my kitchen and one of the lights on one end stays on for about 5 minutes and then turns off for about a minute and then turns on for about 5 minutes and so on . I changed the bulb, but this didn't change anything. Its like somebody is switching it on and off, but the rest of them stay on.

Can lights have a thermo protector that turns them off if they get too hot.

Most often caused by too big of a bulb or a bulb of the wrong type.

Remove the bulb and you will find a lable inside the can that list the size and type of the bulb that can be used.

Often if also depends on what trim ring is used.

If that is not the problems then the thermo protector is bad.

Or it is not an IC (insulation contact rated) can and insulation has been stuffed around it.