A man in his thirties was shot in the stomach at Forum Court near the railway station on Tuesday.
He is in a stable condition in hospital.
A 34-year-old man has been arrested on suspicion of conspiracy to murder and a man, aged 39, was held on suspicion of attempted murder. A man and two women arrested have been released on bail.
A burnt-out car found in Rushbrooke Lane in Bury St Edmunds at 19:15 BST on Tuesday is being linked to the investigation, following the discovery of a shotgun inside it, police added.
A 58-year-old man and two women aged 59 and 28, all from the Needham Market area, were released on bail until 1 October.
All three were arrested on suspicion of conspiracy to murder.
The other two arrested men are from Dorchester.
Two further arrests have been made by police investigating a shooting in Bury St Edmunds.