Dundee will host Celtic while Kilmarnock will make the trip north to face Aberdeen.
The last tie to be drawn was Rangers v Cove Rangers.
All ties are scheduled to be played on Friday, 25 January 2019.
Scottish FA Youth Cup Fifth Round Draw 2018-19
Dundee v Celtic
Hibernian v Queen's Park
Aberdeen v Kilmarnock
Rangers v Cove Rangers
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