The man's wife died on Thursday night while trying to escape but was thrashed by the locals on the spot.
The incident took place when a police team had gone to raid history-sheeter Vikas Dubey's house.
The plea, filed in the apex court by advocate Ghanshyam Upadhyay, has referred to media reports and claimed that encounter of these five co-accused by the police is "not only extremely illegal, inhuman, but also it is shocking to the conscience of the court and is nothing but Talibanisation of the country, which cannot be countenanced at all".
The notices were issued on Tuesday after damage of nearly Rs 25 lakh was assessed across the district by the police and the administration.
Eight police personnel, including a deputy superintendent of police, were gunned down in a village near Kanpur city by the henchmen of a criminal who lost two of them in a firefight later, officials said.
PM Modi, BJP president J P Nadda, Congress leader Rahul Gandhi and Delhi Chief Minister Arvind Kejriwal have all expressed grief over the incident.
At least 62 passengers were on Wednesday injured when 15 coaches of the Sealdah-Ajmer Express derailed while it was crossing a bridge near Rura Railway Station in Kanpur Rural district, the second rail accident in the region in two months.
Railways Ministry spokesperson Anil Saxena said several people have been rushed to nearby hospitals with injuries, and the casualties may go up.