It sounds like you have a gott cooler with an element in the side and a thermocouple or sensor through the lid. With 5 gallons of water and no circulation the response is going to be real slow, shown by the "I" time of 28.5 minutes. Here are some suggestions for an initial manual setup for the PID values P=20, I=180, D=45, SouF=.2, Ot=10(this will increase the minimum on time to 10 seconds). After setpoint temperature is reached watch the time between PV peak values, this is what you need for the I parameter, again use 25% of I for the D parameter. If the controller keeps overshooting the temp then increase Souf by .1, if not overshooting then reduce by .1. With the quantity of water and 1500 watt element you should hit 1.8 deg rise per minute if stirred to distribute heat input, if you are letting the thermosiphon effect distribute the heat then it will be slow to change temperature and harder to control.