How come category 5 hurricanes don't stay at their peak strength for very long?

I think it is combination of the eyewall replacement cycle and the need for very warm water. Category 5 hurricanes are extreme events, and everything has to be just right to stay extreme. To get category 5 winds you need to have both intense low pressure and strong cumulonimbus clouds at the eye, if one or the other isn't there then the winds will decrease. In lower category storms the low pressure alone may be enough to sustain the category wind levels.

I also think it's something of an artifact of the way hurricane intensities are estimated. If there are no flights into a hurricane to make measurements, then intensity is estimated on satellite presentation. To get category 5 you have to have a very impressive satellite image, and if a replacement cycle is underway then the image will not be as impressive.