Local media reported that three young people aged 17, 15 and 12 were struck by an electrical current in the park's swimming pool on Friday.
The park's 58-year-old manager and his 30-year-old son jumped into the pool to try to rescue the children, but were also killed by the current.
Rescuers attempted resuscitation, but it didn't help. All five were rushed to a hospital, but their hearts had already stopped, the hospital told the Daily Sabah newspaper.
An investigation has been launched into what could cause the tragedy. But reports say the park was undergoing renovations and many electrical cables were around the pool, one of which could have fallen into the water. Also, the park lacked a residual current device which breaks an electrical circuit.
Hasan Akcan, the mayor of Akyazi, said the incident was "saddening", according to state-run news agency Anadolu. The park had received a license in 2012 as a swimming pool and amusement center.