PC David Rathband was blinded by Moat in Newcastle on 4 July, 2010 and took his own life in February 2012.
His twin brother Darren said the family were "still fighting for acknowledgement that David was let down" by Northumbria Police.
The force said the family's legal case against it would go to court in 2016.
Family members claim Northumbria Police did not do enough to warn staff that Moat had told a 999 call handler he was hunting for officers on the night of the shooting. The force denies this.
Traffic officer PC Rathband was finishing his shift in a marked patrol car when he was shot twice by a shotgun fired by Moat.
He survived but lost his sight in both eyes.
Moat had shot Samantha Stobbart, who survived, and Chris Brown, who died, in Birtley, Gateshead, the previous day hours after his release from prison.
Following a week on the run, the former nightclub bouncer turned the gun on himself during a stand-off with police in Rothbury on 10 July.
After he was shot, PC Rathband founded the Blue Lamp Foundation to help injured 999 workers, wrote a book about his experiences and became a national figure.
However, he struggled to cope with the consequences of losing his sight and the father-of-two, 44, killed himself at his home in Blyth, Northumberland.
His brother, who lives in Australia, said of the 4 July anniversary of the shooting: "As a family we obviously reflect on past events that had such a tragic outcome for David.
"It means we understand more than most the risks the emergency services, especially police, are asked to face on a daily basis."
He said the dangers faced by officers from acts of terror was "very pertinent" following attacks in Tunisia, France and Kuwait.
"Sadly, David will not be the last police officer injured in the line of duty; three officers have been shot and numerous have been hurt in the UK since 2010," he said.
He said 4 July was a important date for the family, but that the "significant anniversary" was the date of PC Rathband's death when they lost a "very special man".
The family of the police officer shot by gunman Raoul Moat say they are still waiting for justice five years after the attack.