Officials believe four deaths were related to vehicles struck by a tornado that touched down in the southeast part of Garland, police spokesman Officer Joe Harn said.
Details on the fifth death were not immediately available.
There were three additional deaths in Collin County, said Chris Havey, a spokesman for the sheriff's office. He declined to release any more information until authorities can fully assess their situation.
Police said the death toll was a preliminary figure. Garland suffered significant damage, Dallas County Emergency Manager Clay Jenkins said.
Law enforcement officials and trained weather spotters also reported a large tornado near DeSoto, just south of Dallas, Saturday evening.
About an hour later, there was also a report of a tornado in eastern Ellis County, the next county to the south, the Fort Worth office of the National Weather Service said
. It was unclear if it was the same tornado.
There was also damage to a church om Ovilla and homes in DeSoto, Jenkins said.
Other parts of Texas were dealing with other types of hard winds and precipitation, the weather service said.
An arctic cold front will swoop down to the Rio Grande area of west Texas, bringing a nasty mix of snow, sleet and freezing rain from there to New Mexico on Saturday and Sunday, forecasters predicted.
"By Sunday morning, the snow, sleet and freezing rain will expand northeast across the southern Plains," the NWS said.
"Heavy snowfall amounts of 10 to 18 inches are forecast through Sunday evening across much of western/northwestern Texas, with 18 to 24 inches forecast across portions of New Mexico."
Throw in some fierce winds, and parts of the Southwest could see blizzard conditions, the weather agency said. The blizzard conditions could affect people from New Mexico toward the Oklahoma and Texas Panhandles, with 1.2 million under a blizzard warning.
In addition to snow, icy conditions are expected from central Oklahoma up into Kansas with ice accumulation and strong winds, making the roads dangerous for driving.
The weather service office in Norman, Oklahoma
, reported a possible tornado in the southern town of Burneyville.
Four die in Minnesota accident
Four people died in a weather-related car accident in Aitkin County, Minnesota, on Saturday, State Trooper Lt. Tiffani Nielson said.
The accident was one of 204 that happened on snow-covered roads Saturday, she said.
CNN affiliate WCCO
reported the accident involved a Mazda SUV and a Chevy Suburban. Three of the people in the Suburban were seriously injured in the crash, the Minneapolis station said.