Police said the kangaroo court, called 'salisisabha' in the state, was held at Jainpur village in the district yesterday evening.
The attack on the family took place as they refused to part with their land measuring 13 katha for road building purpose.
Of the five, two were critically injured and have been admitted to the Malda Medical College and Hospital. The rest are being treated at the local public health centre.
Police said 15 neighbours have been accused for attacking the family while the kangaroo court was in progress and are absconding since the incident.
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The injured are aged between 34 and 48 years and hail from Jainpur, the police said.
The kangaroo court was called when a member of the family complained to the village leaders that they were being co-erced to give up their land.
Investigation into the incident is on, the police added.