The Toffees’ route to Wembley will continue during the weekend of January 22-24, when they welcome Wednesday, 21st in the Championship, at Goodison Park.
And if they see off the Owls, Everton will host the winner of the fourth round tie between Wycombe and Spurs during the week commencing February 8.
Everton previously met Sheffield Wednesday in last season’s Carabao Cup, when two early Dominic Calvert-Lewin goals sealed a 2-0 third round win for Marco Silva’s side at Hillsborough.
They have already beaten Spurs in this campaign, winning 1-0 at the Tottenham Hotspur Stadium in September, but have never played Wycombe before.
Wycombe sit bottom of the Championship, while Spurs are currently fourth in the Premier League.
Everton beat Rotherham United 2-1 after extra time at Goodison on Saturday to reach the fourth round.
FA Cup - Full Fourth Round Draw
Cheltenham Town vs Manchester City
Bournemouth vs Crawley Town
Swansea City vs Nottingham Forest
Manchester United vs Liverpool
Southampton or Shrewsbury Town vs Arsenal
Barnsley vs Norwich City
Chorley vs Wolverhampton Wanderers
Millwall vs Bristol City
Brighton & Hove Albion vs Blackpool
Wycombe Wanderers vs Tottenham Hotspur
Fulham vs Burnley
Sheffield United vs Plymouth Argyle
Chelsea vs Luton Town
Stockport County or West Ham United vs Doncaster Rovers
Brentford vs Leicester City
Everton vs Sheffield Wednesday
Ties to be played during weekend of January 22-24
FA Cup - Full Fifth Round Draw
Fulham or Burnley vs Bournemouth or Crawley Town
Manchester United or Liverpool vs Stockport County or West Ham United or Doncaster Rovers
Sheffield United or Plymouth Argyle vs Millwall or Bristol City
Chorley or Wolverhampton Wanderers vs Southampton or Shrewsbury Town or Arsenal
Barnsley or Norwich City vs Chelsea or Luton Town
Everton or Sheffield Wednesday vs Wycombe Wanderers or Tottenham Hotspur
Swansea City or Nottingham Forest vs Cheltenham Town or Manchester City
Brentford or Leicester City vs Brighton & Hove Albion or Blackpool
Ties to be played during week commencing February 8