Police in the canton of Valais said two fellow skiers survived the avalanche, which hit Saturday afternoon as they headed for the Fiescheralp area at an altitude of some 2,450 metres.
"According to the investigation, the victims are Spaniards. Formal identification of the deceased is under way," a police statement said, adding that another group nearby managed to raise the alert.
The five swept away were all wearing detection devices, helping rescuers to locate the two survivors and airlift them to hospital.
However, poor visibility hampered an operation which had to be broken off overnight before rescuers recovered three bodies Sunday.
Valais police had Thursday warned that fresh snowfalls and high winds had notably increased the risk of avalanches above 2,000 metres.