Cherry Groce was shot when police raided the family home in Brixton, south London searching for one of her children.
The shooting of the black mother led to the 1985 Brixton riots against police racism and brutality.
The claim against the cops is for damages for the psychiatric injuries the five say they sustained as a result of the shooting.
Four of the five were in the house when the shooting occurred. They also had to witness the suffering of their previously active mother, caring for her for 26 years until she died.
Four of the five were diagnosed with post-traumatic stress disorder following the shooting, which happened when they were eight, 11, 14, 18 and 21 respectively.
The five variously have anxiety, panic attacks and depression.
An inquest held last year found that police failures in planning and implementing the raid contributed to
Cherry’s death. The jury identified eight failings on the part of the Met.
Met commissioner Sir Bernard Hogan-Howe apologised to the family after the inquest, admitting that the police had caused “irreparable damage”.
Lee Lawrence, who was 11 at the time, said, “I was curled up in my mum’s bed, for me the safest place in the world, when I heard a loud banging, which must have been the police breaking the door down.
“My mum went to see what was going on and that was when the police shot her.
“I remember screaming, ‘What have you done to my mum?’ I heard my mum saying, ‘I can’t move my legs, I can’t breathe, I think I’m going to die.’ At that moment everything in my life changed for ever.”
The family is suing the Met for trespass, a catalogue of 22 incidents of negligence, misfeasance in public office and human rights breaches.