The winner of Wednesday rescheduled FA Trophy against Rochdale will make the trip to National League South outfit Worthing.
Worthing are currently 7th in the National League South and were 5-1 winners over Torquay United in their Fourth Round tie on Saturday.
Should Stockton defeat Rochdale on Wednesday, then they face the daunting 640-mile round trip to Woodside Road on the South Coast which would be their longest-ever away day.
The tie is scheduled to be played on Saturday 1st February.