Postpublished at 23:00 Greenwich Mean Time 8 January 2015
That's all for tonight, then, so you can get to your beds.
But remember to join us again at the weekend for more live text coverage of the best European football action.
Goals by Neymar, Luis Suarez and Messi give Barca 3-0 half-time lead
Jordi Alba converts Messi pass to make it 4-0
Neymar adds the fifth with a fierce drive
Messi is reportedly unhappy under boss Luis Enrique
Second leg to be played on 15 Jan
Mike Henson and Richard Winton
That's all for tonight, then, so you can get to your beds.
But remember to join us again at the weekend for more live text coverage of the best European football action.
A quarter-final place looks secure, then, but Barcelona will meet either Atletico or Real in the last eight.
The Spanish champions are favourites, having established a 2-0 lead in the first leg, but the champions of European are at home in next Wednesday's return at the Bernabeu. A thriller awaits.
They might have ambled through this test but a far tougher proposition awaits Barcelona on Sunday when Atletico Madrid come to town, fresh from a 2-0 victory over city rivals Real in the Copa del Rey.
The last time the sides met, Diego Godin's header at the Nou Camp in the final game of the 2013/14 season earned Diego Simone's side a 1-1 draw and the La Liga title.
And, after a pretty sterile final half hour, it's over. Barcelona scored five goals in 25 minutes either side of the interval to make next Thursday's second leg against Elche a formality.
One minute of stoppage time signalled. For Elche, that's 60 seconds too long.
Lionel Messi drops another cute ball behind the Elche defence but, this time, it's substitute Adriano who strayed offside before lobbing the ball over Przemyslaw Tyton.
His goal has been breached on five occasions tonight but Przemyslaw Tyton will have had worse nights in his career. Elche's Polish goalkeeper, on loan from PSV Eindhoven, has made several fine saves to deny Barcelona.
Lionel Messi and Luis Suarez combine devilishly to release Pedro but his scooped effort drops just wide of the target with Przemyslaw Tyton beaten.
That's one way to deal with Lionel Messi... wrap a leg around his waist and force him to the ground. Sergio Pelegrin earns a yellow card for his efforts.
From the subsequent free kick, Przemyslaw Tyton scrambles across his goal to paw Messi's effort away.
Some said he was in the huff, having bickered with coach Luis Enrique at training earlier in the week, but Lionel Messi has been central to much of what was good about Barcelona against Elche.
Final switch for Barca sees callow midfield Sergi Samper gambolling on for a fourth senior appearance in place of Gerard Pique.
Elche have made a couple of changes, too. Neither Aaron Niguez nor Jonathas looked entirely delighted to be exposed to this but Coro and Cristian Herrera have run their race.
Neymar's emphatic finish put Barcelona ahead after 35 minutes and, by the time he was withdrawn by Luis Enrique, the advantage was 5-0.
Pedro scored four goals in the 12-1 aggregate win over Huesca in the last round. And he scored twice in Barca's 2012 final triumph over Athletic Bilbao. He's also scored in a Champions League final.
Perhaps not the man Elche wanted to see come on, you suspect...
Have Barcelona settled for five? Certainly the tempo has dropped a little since Neymar's second of the night and the Brazilian is now trudging off the pitch to be replace by Pedro.
Barca reached the final of this competition last season, only to lose to Real Madrid in extra time. The winner? That astonishing Gareth Bale goal, when he romped down the left after scampering out of play before netting.
First change of the night for Barcelona as Adriano replaces Jordi Alba.
Now that's just outrageous. Neymar is allowed to meander infield by the increasingly woebegone Elche defenders and the Brazilian unleashes a rising shot that scuds against the underside of the crossbar before rippling the rigging.
Ooh, that's delightful. Lionel Messi cleaves open the Elche defence with a fabulous angled pass and Jordi Alba takes a touch before ramming gleefully past Przemyslaw Tyton.
Remarkable scenes! Elche break into the Barca half and play rages towards Marc-Andre Ter Stegen's box...
But the threat doesn't last as they give the ball away cheaply.