The approach of yet another severe winter chill sent natural-gas prices soaring to a five-year high, as investors bet the brutal weather across the U.S. will put further strain on supplies of the heating fuel.

Prices have climbed 45% this year as homes and businesses across the Midwest and Northeast consume record amounts of the fuel to get through a series of cold snaps. That demand is rapidly depleting U.S. gas inventories, which entered the winter near highs. January had the highest average natural-gas demand on record,...