Police have named 32-year-old Anthony Winter as the man found dead in woodlands in Cardiff on Thursday.
Five people are being held on suspicion of his murder, following the further arrest of a 19-year-old woman on Saturday.
The family of Mr Winter, who was from the Pentwyn area of the city, said they were “devastated” by his loss.
They have also urged anyone with information to contact police.
Officers arrested a 16-year-old boy and a man, 27, earlier on Friday and a 17-year-old girl and a 19-year-old man later that same evening.
South Wales Police have said they suspect Mr Winter would have known those who killed him.
His body was found on woodland popular with dog walkers near Brookfield Drive in St Mellons at about 07:15 GMT on Thursday 22 November.
In a statement from his family, they said Mr Winter “may not have been perfect but he was our kind of perfect”.
They said the father of a two-year-old girl had been violently assaulted and “left to die alone”.
“He did not deserve to die that way,” they added.
“We need justice for his daughter so that our brother can rest in peace.”
South Wales Police said it was not looking for any more individuals in connection with the death, but renewed its appeal for those with any information to come forward.
Det Supt Richard Jones, who is leading the inquiry, added: “I would like to reassure his family and the wider public that we are committed to tracing and bringing to justice all those involved in taking this young father’s life.”