Each term in the series is multiplied by 3, and then an increasing integer is added. The first term 5 is multiplied by 3 and added to 0 to get 15, the second term 15 is multiplied by 3 and added to 1 to get 46, and the third term 46 is multiplied by 3 and added to 2 to get 140. Following this pattern, 140 is multiplied by 3 and added to 3. The result is 423.