When they passed through security checks on June 13, officers found $352,000 and EUR245,900 ($269,000) hidden in their luggage, Cong An Nhan Dan newspaper reported.
They are investigating.
According to the police, the five arrived on two different flights from Poland that transited in Doha.
People carrying more than $5,000 into or out of Vietnam have to declare it to customs. Failure to do so is a crime that carries a maximum of 10 years' imprisonment.