The Black Cats beat Shrewsbury 3-1 on Wednesday night to set up the tie against the Magpies, who won by the same scoreline against Swansea on Monday evening.
Substitute Thomas Allan scored twice while Lewis McNall was also on target from the spot for United under the St. James' Park lights.
The draw was made last week so both clubs knew that a derby clash awaited if they could progress in their respective fourth round matches.
Fifth round ties must be played by Saturday, 4th February. Sunderland are one of a handful of clubs who have FA approval to play home matches at an alternative venue to their home ground. Their fourth round tie was played at Eppleton CW.
In February 2015, Newcastle travelled to the Stadium of the Light in the fifth round and won 3-1 on penalties after a 0-0 draw. And the year before, United ended their local rivals' interest in the competition with a 4-0 win at St. James' Park.