An anti-terror court in Lahore convicted the group for the killings of Shahzad Masih and Shama Bibi in 2014 after the pair were accused of blasphemy.
Eight other men who were part of a group of more than a hundred involved in the attack have been jailed for two years.
Shahzad Masih, 26, and his 24-year-old wife Shama Bibi, who was four months pregnant, were beaten, tortured and burned alive in a furnace.
They were attacked by a mob of Muslims after a claim they had ripped up a Koran was shouted from mosque loud speakers.
A total of 103 people were charged in connection with the crime but late on Wednesday just 13 were convicted. The rest were freed.
The owner of the furnace was freed and will face no charges.
Judges ordered the five men to be killed by hanging and imposed fines of around £1,500 that their family will have to pay.
The lawyer representing the couple's family, Riaz Anjum, said: "The five people awarded the death sentence were involved in dragging, beating and burning the couple while the other eight played a supportive role according to the judgement."
Mukhtar Masih, father of Shama Masih, said: "We were unable today to attend the court today due to the risk to our safety.
"I am disappointed with today's result as my eldest daughter Yasmeen, who saw the whole incident witnessed at least 15 men involved in the brutal violence against my daughter Shama and her husband Shahzad.
"Only five of those men have been convicted with a death sentence yet the others poured kerosene over Shama and Shahzad and were also violent.
"Two years imprisonment for those who were involved in a lesser capacity for a crime that lead to two deaths seems too lenient."
