Two penalties from Luka Modric and Rodrygo made it 2-0 at half time and then goals from Marco Asensio, Vinicius Jr and Fede Valverde put Celtic to the sword in the second half.
A consolation freekick from Jota got one back for Celtic at the end.
It only took Real Madrid six minutes to get ahead and put themselves in pole position to top the group.
A shot from Marco Asensio hit the outstretched arm of Mortiz Jenz in the box and there was no option for the official than to give a penalty.
Modric stepped and calmly dispatched the spot-kick and settled any nerves about losing top spot that the watching fans may have had.
After a couple of promising moments for Celtic, Asensio was released down the right and played the ball across the box for Vinicius Jr at the far post. He saw his low shot saved though by Joe Hart.
The ball came to Rodrygo who tried to shoot but the ball hit Matthew O'Riley in the arm and another penalty was awarded after 20 minutes.
It was Rodrygo who stepped up and he found the bottom corner and made it 2-0.
Six minutes into the second half, the game was truly wrapped up as Asensio got a goal that his play deserved.
Valverde played it wide where Dani Carvajal could lift it to the edge of the box. Asensio then sidefooted it into the bottom corner calmly.
It swiftly became 4-0 when Valverde played a superb cross into the box where Vinicius Jr was waiting to flick it into the back of the net.
Five star Real Madrid
The rout continued with a goal from Valverde with 20 minutes to play. The midfielder certainly deserved to get a goal after a great display.
The next action was a superb freekick from Jota to give the Celtic fans something to cheer about and make it 5-1.
Real Madrid finish the group with 13 points, joined by RB Leipzig in the second round. Celtic are out of all European competition and Shakhtar Donetsk have gone into the Europa League.
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