Neil Winskill's side secured an impressive 4-1 win against Leeds United in round four, with Dylan Stephenson's first-half hat-trick and Joe White's strike sealing a well-deserved victory at Whitley Park.
Their reward is a home tie against the Hornets (kick-off 2pm BST), who progressed into the fifth round stage following a 3-2 away win against Lincoln City after extra-time.
The young Magpies will be bidding to reach the quarter-finals of the competition for the first time since 2017 and, should they advance past Watford, will face another home clash against either Aston Villa or Burton Albion in the last eight.
Newcastle's youngsters have won the competition twice in their history and will be aiming to lift the trophy for the first time since a Paul Gascoigne-inspired United won the tournament back in 1985.