The Taliban militia, who have mounted a bloody insurgency since they were forced out of government by US-led forces in 2001, claimed late on Wednesday to have captured the five.
The governor said a search operation by about 200 security officials for the missing people in Khad Rod district had been called off Saturday after the troops failed to locate them.
"Most of our troops have returned and the operation has been called off. We conducted a very massive operation including searching suspected houses but we couldn't find them in the area," he said.
Helmand province, where the intelligence reports say the hostages have been moved to, is a Taliban stronghold where the rebels hold several districts.
An Italian journalist was kidnapped March 5 by the Taliban in Helmand province, which adjoins Nimroz.
Daniele Mastrogiacomo was released two weeks later in a controversial deal.
The Taliban are still holding Mastrogiacomo's translator, Afghan reporter Ajmal Naqshbandi, and have demanded the release of two more Taliban in exchange for his freedom. The rebels beheaded a driver captured with them.
The rebels are also holding five Afghan medics they kidnapped on March 27 in the southern province of Kandahar.