Take out the roast 4 hours before cooking to bring the roast completely up to room temperature. Trim any excess fat from the roast.
30 minutes before cooking set oven temperature to 500°. Combine butter, garlic, salt, pepper, and herbs in a bowl and mix to combine.
Coat prime rib with garlic and herb butter completely and place in a cast iron skillet or roasting pan with rack fat side up.
Cook in preheated oven for 30 minutes for a 5 pound roast. Once that time is over, turn the oven off and leave in for 2 hours. Keep the residual heat inside the hot oven by not opening the oven door at all.
Take out of the oven and insert a meat thermometer in the center of the roast and check the internal temperature for desired doneness. 130°-135° is a perfect medium-rare prime rib and 135°-145° is a medium prime rib. It continues to increase in temp by 5-10 degrees while resting so take that into account. If it is not to the temp you'd like (because ovens are different), turn oven on to 375° and cook until the desired temp is reached.
Remove roast from the pan and rest covering with aluminum foil for about 20 minutes. Again while it rests the temperature will increase so check with a digital thermometer to keep track so it's not over cooked.