The victim Hu Congliang, 20, is believed to have been dating one of the five in Modena, a city in northern Italy near Prato, where there is a very large Chinese community.
When the 17-year-old boyfriend tried to break up with him, Hu allegedly threatened to make public intimate photographs of the minor he had saved on his telephone.
"From what we understand so far, the punitive mission was prompted by the photographs," deputy police chief Marcello Castello told the media.
"All five say they don't speak Italian, which we don't believe. They are all underage and have been utterly impassive. Just like their parents, who have been completely uncooperative," he said.
The 17-year-old is believed to have summoned his gang to Hu's house on Sunday. There they ran into his mother and her partner, but went into the youth's bedroom to chat.
There they are believed to have smothered Hu with a pillow before emptying a suitcase found under the bed and stuffing his body inside. They then said goodbye to his mother, saying her son had left the house earlier.
She made the grisly discovery hours later, after her son failed to return and she noticed the suitcase out of place.
One of the five turned himself in to police voluntarily, the other four were arrested, one while playing video games.
Coupling the Chinese murder with the recent suicide of an Italian youngster who feared sexual images of her would be made public, Piazzoni slammed "a culture that tarnishes sexuality and sexual orientation".
"The issues of sexuality, sexual orientation and sexual practices are still taboo in our country... and yet it is this very stigma that hands violent people their lethal weapon," he said.