Galeno scored twice in the first half to put the home side in command at the interval, before second-half strikes from Wendell, Pepe and Danny Namaso turned it into a rout against the 10-man visitors.
The result is Porto's joint-biggest ever league victory in O Classico, and their biggest since winning by the same margin in the 2010-11 season.
Benfica had been knocked off top spot in the Primeira Liga table less than an hour before they kicked off as a result of Sporting Lisbon's 3-2 triumph over Farense.
The defending champions' day only got worse from thereon in, with Galeno opening the scoring after only 20 minutes and doubling his personal tally shortly before half time.
Wendell made it 3-0 as his deflected strike from the edge of the area bobbled into the bottom corner, before Benfica's slim hopes of getting anything out of the game suffered yet another blow as Nicolas Otamendi was sent off for a second bookable offence.
A fourth arrived 15 minutes from time as Pepe blasted his finish in at the near post from a tight angle, with Benfica keeper Anatolii Trubin at fault as he attempted to anticipate a shot across goal instead.
Porto then added a fifth when Namaso capped off the scoring in the final minute of normal time, ensuring that they equalled the biggest margin of victory in a league game between the two great rivals since 1942.
The result means that Benfica remain second in the table, now one point behind new leaders Sporting, while Porto keep their own title hopes alive with seven points now separating them from top spot.