The result marked a disappointing start for the Swiss champions in the opening game of the Group B qualifying series for the Champions Cup.
The team’s coach Paulo Sousa said ahead of the game he believed his team could trouble Real Madrid, as well as Liverpool, which it takes on in two weeks time.
“We want to build on what the club has done in the last five years, continue to progress and compete with the best,” he said.
But Real Madrid, the Champions League champions who have faced their own struggles recently, losing two Spanish league games and the Spanish Super Cup, proved to be too strong for the Basel squad.
The Swiss team started off badly when Marek Suchy scored an own goal in the 14th minute when a cross deflected off him into the net.
By half-time, the battle was already lost as Gareth Bale scored for Real Madrid after 30 minutes followed by a goal from Cristiano Ronaldo a minute later and another from James Rodriguez at the 36th minute mark.
Derlis Gonzalez potted Basel’s only goal a couple of minutes later while Karim Benzema scored Real Madrid’s fifth goal late in the second half.
Basel coach Sousa was left to rue his side's weakness in defence despite showing flashes of their quality on the ball.
"We created chances, we were brave to have the ball and didn't just look to defend," he said.
"In certain moments we were too naive, but in other moments we showed good quality and personality."