They were first arrested in June last year on charges of apostasy, holding political meetings, and committing blasphemy and crimes against the Islamic Order.
The Revolutionary Court in Shiraz found the five men guilty of crimes against the Islamic Order and sentenced them to one year’s imprisonment.
They served eight months of their sentence before being released in February on bail.
Their lawyer has appealed the one-year prison sentence and a decision is pending.
It had been presumed that the other charges against the men had been dropped but a source close to them confirmed that they are to stand trial for blasphemy.
CSW’s national director Stuart Windsor said he was “dismayed” by the charges levelled against the group.
“The international community must press Iran not only to rescind the unjust punishments to which these Christians have already been subjected, but also acquit them at the upcoming trial,” he said.
CSW said the situation for Christian in Iran was worsening, with churches finding it difficult to hold meetings and many considering leaving the country.
It expressed concern for Yousef Nadarkhani, the pastor of a large church in Rasht, who was arrested in 2009 and later sentenced to death for apostasy.
As there are no articles in the Iranian legal code criminalising apostasy, the judge based his ruling on texts by Iranian religious scholars.
Nadarkhani remains in prison and his fate is uncertain as he awaits the outcome of an appeal filed at the Supreme Court last December. A hearing is due to take place in the next two months.
Mr Windsor called upon Iran to guarantee religious freedom for all its citizens.
He said: “We are concerned that the judgement handed down in Pastor Nadarkhani’s case did not follow due procedure under Iranian law.
“As a signatory to the International Covenant on Civil and Political Rights, Iran has an obligation to uphold international standards of religious freedom for all its citizens, to follow due process and refrain from arbitrary judicial rulings based on open-ended legislation.”