The blaze broke out on Monday evening in a storage room of the five-storey building in the town of Manlleu, around 80 kilometres (50 miles) north of Barcelona, the service said in a statement.
"Five people died this evening and four others sustained minor injuries," the firefighters said.
The victims have been described in the Spanish press as "teenagers". According to Spanish national broadcaster RTVE, town hall sources reported that the victims included three minors who were 12, 15, and 16 years old.
Firefighters explained that they were alerted by neighbours to the presence of smoke in the stairwell and that, once the fire was extinguished, "the first victim was located, a person in cardiorespiratory arrest".
"Then four more (people) were found in the storage room" and "it was not possible to save them", they added.
Of the four people injured, three were able to leave the hospital after receiving treatment and a fourth did not want to be transported to a care facility.
"For reasons unknown, the people inside were unable to get out" of the storage room and "nothing could be done to save their lives" despite the intervention of firefighters and ambulances, emergency service said.
There are reports that the storage room had reportedly been turned into a housing unit, but this is yet to be verified.
Police have opened an investigation.
Catalan regional president Salvador Illa has expressed his shock at the death of the five young people in Manlleu, conveying his condolences to "their families and friends" while wishing a speedy recovery to the injured.
With additional reporting by Alex Dunham, The Local Spain's Editor
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