Wilfred Isaacs, 50, died at the Chubbards Cross caravan site near the village of Ilton on Thursday evening.
Three people are being held in custody on suspicion of murder, attempted murder and assisting an offender.
Police later arrested another suspect, John Broadway, 37, in Lichfield, Staffordshire, along with two women held for assisting an offender.
Mr Broadway was being questioned on suspicion of murder, attempted murder and firearms offences.
Police are still searching for Donna Broadway, 26, as well as the weapon used in the crime.
Other suspects arrested earlier are:
Det Supt Andy Bevan, of Avon and Somerset Police, said officers believe a shotgun was used and appealed again for information from the public.
He added there was still a "major rapidly evolving investigation" involving officers searching for Donna Broadway.
"Our enquiries are not confined to the Avon and Somerset Force area and we're following up all possible leads as they materialise," he said.
Police said the caravan site would be closed off as inquiries are likely to last several days.
A man who was killed in shooting at a Somerset caravan park has been identified.