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League Two Newport County secured a 1-1 draw with Championship promotion-chasers Boro at the weekend to secure a replay at Rodney Parade, South Wales.
The replay will take place on 5 February at 7.45pm.
The fifth round ties will be played over the weekend of 15 to 18 February.
City have only ever played Newport - who saw off Leicester City in the third round - on three occasions, the last being a 2-1 win in 1962.
The Blues have won all three meetings, two being league matches and one in the League Cup.
City and Boro have locked horns many times over the years, with overall meetings seeing the Blues marginally ahead with 51 wins to Boro's 49.
The teams have met on numerous occasions in the FA Cup.
The first was back in 1904 when the Hyde Road clash ended 0-0 - but City won the replay 3-1.
It would be 68 years before the next FA Cup tie, with Boro again securing a draw - this time 1-1 - in 1972 - and Boro won the replay 1-0 at Ayresome Park.
Boro won the next two meetings in the FA Cup - a 2-1 win in 1992 and 1-0 win at Maine Road in a fifth round tie in 1997.
A Benjani winner have City a rare Riverside Stadium win in 2010, but the Boro jinx struck again in 2015 when defending Premier League champions City were knocked out at the fourth round stage after a 2-0 defeat at the Etihad to the then Championship side.
The date and ticket details will also follow in due course.
The full draw is:
Brighton/West Brom v Derby County
Portsmouth/QPR v Watford
Swansea City v Barnet/Brentford
Chelsea v Manchester United
Doncaster Rovers v Crystal Palace
AFC Wimbledon v Millwall
Bristol City v Shrewsbury/Wolves
Middlesbrough/Newport v Man City
Pep Guardiola previews City's trip to Newcastle United
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