Eko Hot Blog reports that Police found the bodies on Wednesday while conducting a welfare check at the property, about 245 miles (394km) south of Salt Lake City.
No motive for the killings is known and police have not given details about those killed.
City leader Rob Dotson said the city of around 8,000 people was in shock.
“This community at this time is hurting. They’re feeling loss, they’re feeling pain and they have a lot of questions,” Mr Dotson said.
He added that the family was well-known in the town, and that police would release further information as the investigation continued.
Reports claim that the five children attended schools across the Iron County School District.
Utah Governor Spencer Cox tweeted his condolences for those affected by the “senseless violence”.
Source: BBC
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