Two other injured men were taken to hospital, where a 25-year-old with knife wounds is in a critical condition, West Midlands police said.
A 22-year-old is being treated for gunshot injuries that are not thought to be life-threatening.
Four of the arrested men are suspected of violent disorder, and the fifth man of possessing a class-A drug.
The dead man has been named locally as Ikram Elahi.
One witness claimed "about 200 to 300 lads" had gathered in the area around Stratford Road in Sparkbrook prior to the killing on Wednesday evening.
'Pool of blood'
The A34 Stratford Road was closed throughout Thursday morning but reopened at lunchtime.
Farm Road and Grantham Road remain sealed off as part of the police investigation.
Supt Bas Javid, from Birmingham East Police, said it was unsettling for communities when guns or knives are used.
"There is nothing to suggest there will be any further issues," he said.
"We would encourage people not to speculate and I would reiterate that there is nothing to suggest this will spark any further disorder."
Following a private meeting held for residents at the Christ Church centre on Sampson Road,  Mohammed Ashraf, a member of the Sparkbrook Faith Forum, said: "We urge all families to look carefully into their hearts in this holy month of Ramadan and hand in any information they have.
"Any individuals involved in this, could they please report to the police."
One shopkeeper, who did not want to be named, said he had been leaving the area on a bus when he spotted the scene.
"I saw a man lying in a pool of blood by the side of the road," he said.
"People were surrounding him and trying to help. I didn't understand what I was seeing, whether he had been shot or stabbed.
"It has made me scared. I'm worried about my shop."
Ann Taylor, who lives locally, said she also was worried about the area: "I'm not surprised what happened here really, it's not very nice.
"I'm not very happy now. I feel like I can't go out at night any more. "
A second shopkeeper, who also did not want to give his name, said he had been locking up for the day at about 19:20 when he saw a "large group" had gathered.
"There were about 200 to 300 lads hanging around, it was a large number," he said.
"Then after that lots of police came down.
He added: "It does happen around here, groups fighting among themselves.
"You do see large groups of young lads hanging around, but it doesn't usually escalate to this kind of violence."
Birmingham City Councillor Mariam Khan said: "Any loss of life is a waste, especially young life."
She said, as chair of the social cohesion and community safety committee on the council, she would look closely at issues around gun and knife crime and "focus on what makes young people turn to violence".
Parish priest of the Small Heath area of Birmingham, Father Oliver Coss, offered his condolences and said: "The only thing we harvest from the guns and knives on our streets is another generation of orphans and widows."
A post-mortem examination will take place in due course to determine the cause of death, officers said.
Five men remain in police custody in connection with the fatal shooting of a 28-year-old man in Birmingham.