Their appeal follows last month's out-of-court settlement with 14 officers who suffered psychological illness after struggling to save fans from being crashed to death in pens at the Leppings Lane end of the Sheffield stadium.
Pc Mark Bairstow, Pc Anthony Beavis, Pc Geoffrey Glave, Sgt Janet Smith and Insp Henry White, attended to the dying and dead outside the Leppings Lane enclosures where the tragedy took place.
A sixth officer in the original case has decided not to mke an appeal.
The three defendants to the action - South Yorkshire Police, Sheffield Wednesday Football Club, and the club's engineers - have admitted liability for negligence. But Mr Justice Waller ruled last April in respect of the six that they were not close enough to the scene of the tragedy to be entitled to compensation.
Claims from a further 17 officers will depend on the outcome of the two- day appeal, the first time this area of the law reached the Court of Appeal.
Benet Hytner QC, for the five, urged the Lords Justices Rose, Henry and Judge, to rule that the judge had been wrong to hold that the relationship between the officers and their chief constable did not give rise to a duty not to expose them to a foreseeable risk of psychiatric injury. Further, he also ruled incorrectly that different considerations applied in the case of a rescuer who suffered psychiatric damage from those which applied to a case of physical injury, Mr Hytner said.
The officers' solicitor, Simon Allen, said outside the court: "They accepted the reasonable risks of their service, but they should not be expected to deal with the appalling consequences of the negligent actions of others." A ruling in favour of the officers will, however, re-ignite anger among bereaved families of the 96 dead fans - many of whom received either only modest compensation, or none at all, under the law.
The House of Lords has ruled that relatives suffering post-traumatic stress after watching the horror unfold on television, or at the Hillsborough ground, or at the mortuary some hours later, have no claim in law.Reuse content