Playing at Chester-le-Street, City produced a spirited first half display against the league leaders and were encouraged to be going in to half time only 1-0 down after recent their recent form.
However, Chester le Street returned after the break with added determination, and added two quick goals. Durham rallied and stopped the goals from flowing until the final five minutes.
As Durham pushed forward for a consolation goal, Chester-le-Street added a further three goals.
Based on Durham's performance, they could consider themselves slightly unlucky to be on the receiving end of such a heavy scoreline.
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