The young Glovers take on Boro at Goffs Lane on Wednesday, January 11th (7.30pm).
Tickets for the match in Hertfordshire are priced at £5 for adults, £2.50 for under-16s and concessions, and £1 for under-12s.
Yeovil’s youth side progressed to the fourth round with a giant-killing win over Premier League outfit West Brom at the Hawthorns.
The draw for the fifth round was made today at Wembley Stadium, with ties to be played before Saturday, February 4th.
Full FA Youth Cup fifth round draw:
Birmingham City/Chelsea v Sheffield Wednesday/Gillingham
Blackburn Rovers/Aston Villa v FC Broxbourne Borough/Yeovil Town
Manchester City/Liverpool v Wigan Athletic/Southampton
Middlesbrough/Fulham v Leicester City/Carlisle United
Preston North End/Everton v AFC Wimbledon/Hull City
Queens Park Rangers/Tottenham Hotspur v Burnley/Norwich City
Stoke City/Nottingham Forest v Brighton & Hove Albion/Cambridge United
Sunderland/Shrewsbury Town v Newcastle United/Swansea City