Police nabbed Md Shafiullah, 38, from Hotel Lord's Inn at the port city's Nasirabad on Sunday morning.
The four others are Pakistani Mohammad Alam, 44, Salamat Ullah, 40, Mohammad Amin, 53, and Abdul Majid, 31.
Shafiullah had contested the last Upazila Parishad election with the ruling party's support.
Police suspect the five were connected with Rohingya Solidarity Organisation (RSO) which allegedly is involved with Rohingya militants.
However, one of Shafiullah's party leaders claimed the man had gone to that hotel to discuss about selling land.
But detectives said they were interrogating all the arrestees considering their poosible ties to the Rohingya militants and their activities in Cox's Bazar and Naikhyanchharhi.
Allegations have it that some Rohingya refugees are involved in criminal activities abroad by obtaining Bangladeshi passports.
Indian intelligence officials recently arrested RSO member Khalid Mohammad alias Khalid from Hyderabad over the Oct 2 Burdwan blast in West Bengal.
According to them, Khalid had confessed to have received militant training from Pakistan's Tehrik-e-Insaf on behalf of Myanmar outfit Tehrek-e-Azadi Arakan.
bdnews24.com's investigation also found out that Naikhyanchharhi Upazila resident Shaifullah had connections with the RSO.
Locals said his father Saleh Ahmed was also involved in RSO-related activities in the past.
The local influential family has close ties with the Rohingya people who have illegally come to Bangladesh from Myanmar.
Several local residents also said Naikhyanchharhi AL unit's Human Resource Affairs Secretary Shafiullah works for a faction of the RSO.
They said Shafiullah joined Islami Chhatra Shibir, the Jamaat-e-Islami’s student wing, after passing SSC from Naikhyanchharhi High School. He passed HSC from Chittagong College.
He enrolled at Chittagong University's Bangla department, but did not continue studies. He later passed degree from Nangolkot College and completed masters from a private university in Dhaka.
He is currently working at Naikhyanchharhi's Haji MA Kalam Degree College's political science department as an honorary teacher.
Local journalists said Shafiullah was also the president of the board of directors of two schools and a madrasa there.
A local Awami League leader, asking not to be named, told bdnews24.com that Shafiullah was not even involved in party activities six-seven years ago.
He joined Awami League after working for his brother-in-law who contested the 2009 Upazila Parishad election for chairman.
Naikhyanchharhi Upazila AL unit General Secretary Taslim Iqbal said Shafiullah was not involved with any militant organisation.
He told bdnews24.com that the party leader went to Chittagong to discuss about selling his personal land.
Shafiullah ran for chairman in this year's Upazila polls, but was defeated by BNP-led alliance backed candidate Tofayel Ahmed.
BNP leader Ahmed is one of the accused in a case filed over the rampage in a Buddhist village in Cox's Bazar's Ramu Upazila.
Salamat Ullah, arrested with Shafiullah on Sunday, was also allegedly involved in the arson and vandalism at Ramu.
Salamat is locally known as a chief organiser of RSO in Cox's Bazar.
Another arrestee, Majid confessed to police that his parents were of Rohingya origin.
His passport showed that he was born in Saudi Arabia's Makkah. He visited Thailand, India, Qatar, Bahrain and Turkey in past one year.
Pakistan national Mohammad Alam's father is one Md Yasin of Karachi, according to his passport which police have confiscated.
He has come to Bangladesh for the second time in the past one year.
A huge number of Rohingyas are living at Naikhyanchharhi, near to Myanmar's border, in Bandarban for long.
RSO has long been working at the remote hill tracts Upazila and sponsoring Rohingya militants, detectives have claimed.
Chittagong Metropolitan Police's (CMP) Detective Branch (DB) also suspect that the other four had met Alam at that hotel as RSO 'contacts'.
Alam is the director of Netherlands-based voluntary organisation Global Rohingya Centre, police say.
According to his passport, he arrived in Dhaka on Friday from Jeddah.
He came to Bangladesh on Mar 20 and left four days later. On both occasions, he collected Bangladesh visa from Jeddah.
Also, he visited Saudi Arabia, Thailand, Myanmar, Bahrain and Sudan in past 12 months.
CMP DB Deputy Commissioner Kusum Dewan told bdnews24.com that they were considering different angles while questioning the five arrestees.
CMP have also formed a seven-member team to conduct the interrogation that began on Sunday afternoon.
A DB official, seeking anonymity, told bdnews24.com that they were looking for details about the arrestees' connection to Rohingya militants of Cox's Bazar and Naikhyanchharhi.
The official said they were also trying to find the reasons behind Alam visiting Bangladesh twice in a year during the questioning.