The FA Youth Cup tie with Newcastle United at the Boleyn Ground has been set for Wednesday 3 February with ticket prices mirroring those in the fourth round.
Adult tickets will cost £3 and juniors £1, with all tickets being sold from the cash turnstiles on the night. Entrance to the Boleyn Ground will be through the West Stand lower only.
The Hammers won through to the last-16 for the first time since 2006 by beating Queens Park Rangers 3-0. Colombia-born Cristian Montano scored a brace, while England Under-17 striker Robert Hall got the other.
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West Ham have won the FA Youth Cup three times since its inception in 1953, lifting the trophy in 1963, 1981 and 1999, when the Hammers secured a record 9-0 aggregative victory over Coventry City in the final.
Newcastle United reached the fifth round courtesy of a 3-1 victory at Reading on 13 January.
The match will kick-off at 7pm with cash turnstiles opening an hour before kick-off. Fans are advised to arrive in plenty of time to get tickets before the start of the game.