The families have been given permanent accommodation, and English lessons are being provided to those who need them.
Further numbers of refugees are staying at hotels in the district as they await proper homes.
Speaking at a full council meeting on Wednesday, the authority's leader Denise Jeffery said: "We do have some Afghan refugees who are in hotels, waiting to be processed.
"We are hoping to offer them accommodation, working with WDH (Wakefield District Housing).
"At the moment we only have five families settled, but we are expecting to take more.
"The government are helping us with the funding."
Local Democracy Reporting Service