In each case, masked men, one carrying a handgun, carried out the robberies just a few minutes before their victims were due to close for the day.
They threatened staff with a handgun before escaping with cash or cigarettes.
On three occasions the gun was fired but nobody was injured. It is now believed to have been a replica.
The first target, a shop in Uppingham Road, Leicester, was robbed at 8.15pm on Friday.
Detectives believe the gang then struck three times the next day – beginning at the Local Convenience Store, in Humberstone Lane, Thurmaston, at 8.10pm. About 35 minutes later, they burst into a shop in Leicester's Saffron Lane.
An hour later, at 9.45pm, they robbed a shop in Cardinals Walk, Netherhall.
Officers increased patrols in the Leicester area following the robberies on Saturday, which resulted in the arrest of four people in connection with the Houghton on the Hill robbery - three boys, one aged 17 and two aged 16, and a woman, aged 25. Two of the arrested boys, aged 16 and 17, have been further arrested in connection with the robberies in Uppingham Road (Leicester), Humberstone Lane, Saffron Lane and Cardinals Walk, and remain in police custody. A 16-year-old boy and the 25-year-old woman have since been released without charge.It is understood the five shop robberies are not being linked to Saturday's robbery at Santander, in Leicester's Narborough Road, or an earlier robbery at the bank's branch in Woodgate, on Wednesday, October 3. A cash in transit robbery at De Montfort University on October 9 is also under investigation.
Anyone with any information about the incidents is asked to contact police in on 101. Related article: Five armed robberies on shops in Leicestershire in just 48 hours