Four men entered a house in Cotmanhay and threatened the people inside before stealing cash and tobacco, police have said.
No one was injured in the incident, which police are calling an aggravated burglary, at about 5pm yesterday (Wednesday July 3) in Bennerley Avenue.
Derbyshire police circulated details of the car in which they drove off in and Lincolnshire Police discovered a vehicle matching the description parked outside a house in Gainsborough.
They arrested three men and two teenagers inside the house on suspicion of aggravated burglary.
The five prisoners were transferred to custody in Derbyshire, where they remain.
The men, aged 21, 21 and 23, are being questioned by officers. The 16-year-old boy and 17-year-old girl are also being questioned.
Anyone with information should call police on 101 or Crimestoppers on 0800 555 111.