Remove chilled roast from the refrigerator about 3 hours before cooking. Should be at room temperature when cooked.
Preheat the oven to 500 degrees Fahrenheit.
Add the herbs, garlic, salt, and pepper to the olive oil in a small bowl or measuring cup. Mix together.
Place prime rib in a roasting pan bone side down and fat side up. Pour about ¼ inch of beef stock in the bottom of the pan.
Rub the olive oil and herb mixture on the top and sides of the prime rib and put it in the oven.
Cook at 500 degrees for 15 minutes to brown the outside.
Reduce the temperature to 325 degrees and cook 15 minutes for every pound. For 5lb, 1 hour and 15 minutes for a medium rare prime rib or until it reads 125-135 degrees on a meat thermometer.
Use a meat thermometer to test the prime rib after 30-45 minutes of cook time. Baste with a little of the stock after you check the temp each time (every 20-30 min).
When it has reached the proper temperature, take the prime rib from the oven and place it on a cutting board to rest for 30 minutes.
Cut away the strings holding the roast together and remove the ribs from the bottom.
Carve the prime rib in thin slices across the grain of the meat to serve.