The report comes as Palestinians prepare to mark Prisoners' Day Wednesday, the Palestinian News Agency WAFA reported.
The 5,000 prisoners are in prisons, jails, detention centers and interrogation centers.
The Prisoner Club said 106 of the inmates have been detained for more than 20 years, and 50 of them have been detained for more than 25 years.
The report said Israel can detain Palestinians indefinitely without legal counsel or a court hearing, WAFA said.
The organization also accused Israeli authorities of neglecting the health of prisoners and keeping them in solitary confinement.