Philippe Coutinho opened the scoring, Arturo Vidal bagged the final goal, and in between, there was a superb hat-trick from the outstanding Luis Suarez.
The first Clasico without both Lionel Messi and Cristiano Ronaldo since 2007 leaves Barca back on top of La Liga and Real down in ninth place.
Ernesto Valverde's men were particularly dominant in the first-half as Ivan Rakitic and summer signing Arthur helped midfield maestro Sergio Busquets to run the show.
The Spaniard is never fazed in possession, and he produced another moment of effortless class to get the better of compatriot Isco in the 37th-minute.
Busquets' role in El Clasico
In the absence of Messi, who missed the game due to fracturing his arm earlier this month, Busquets was given the captain's armband and led his side to victory.
Marcelo got Madrid back into it after the interval and the visitors were much-improved, which meant Busquets' role of controlling the tempo became even more important.
He drew praise in the 2-0 win against Inter Milan for casually flicking the ball over two opposition players in the space of seconds, and he dished out some more magic on Sunday.
Busquets leaves Isco for dead with pure class
With the score at 2-0, Sergi Roberto played a pass to Busquets in the centre-circle and he was immediately closed down by Isco.
However, after a quick look over his shoulder, the 30-year-old sent the Madrid man in the completely wrong direction and pulled off a skilful Cruyff turn to move into space.
If that wasn't enough, Busquets then pinged a perfect long-range pass which allowed Jordi Alba to race down the left-wing and put the Champions League holders under more pressure.
Talented playmaker Isco must be sick of the sight of Barca's defensive midfielder when you consider an extremely similar moment in a Clasico from a couple of years ago.
Busquets, who's played a whopping 496 times for Barca, now turns his focus to the upcoming games with Cultural Leonesa, Rayo Vallecano and a trip to Inter.
As for Isco, his side and manager Lopetegui are in somewhat of a crisis, having lost five of their last seven matches in all competitions.
What are YOUR thoughts on Sergio's lovely skill to beat Isco during the 5-1 Clasico win? How far ahead of Real do YOU think Barca are? Have YOUR say in the comments box below!