Redknapp and chief executive Peter Storrie are among those held on suspicion of conspiracy to defraud and false accounting.
Rangers player and Senegalese international Amdy Faye was also arrested in Glasgow.
Police refused to give details of those arrested and would only confirm they were aged 69, 60, 55, 48 and 30.
The men were held as officers carried out raids on 12 locations across the country. Two of those searches are still ongoing.
Detectives from the economic crime unit of the City of London Police are investigating allegations of corruption within football and its impact on owners and shareholders.
A spokesman for Portsmouth said on Wednesday that the club's chief executive and manager had "been asked to help police with their inquiries concerning a matter dating back to 2003".
"This was prior to the new owner taking control of the club at the beginning of 2006," he said.
"The club is fully supportive of Peter and Harry who are co-operating fully with City of London Police in this ongoing inquiry.
"Both are playing major roles in the continued success of Portsmouth Football Club."
Rangers FC have confirmed that a player has been arrested in a matter unconnected to the club.