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This story notes that the failure of the Long March 5 launch occurred 30 minutes after launch, when the second stage and the satellite were due to separate.
The link also includes footage of the launch through first stage separation and ignition of second stage engines.
It appears therefore that the failure was not in the Long March 5 rocket itself. When satellite separation occurs the second stage has completed its work, so the rocket apparently did its job getting the satellite into orbit. What happened next however remains unknown.
Based on this information it would appear that this failure might not delay later launches of the Long March 5 that much.