Five of the nation's major retailers yesterday reported sharp earnings increases for the first quarter as consumer demand picked up in virtually every sales area.

K mart Corp., the nation's second-largest non-food retailer, posted first-quarter earnings of $44.6 million (35 cents a share), about seven times higher than the $5.9 million (6 cents) the company earned in the same period last year, the firm said in a statement yesterday.

J.C. Penney Co. Inc., the nation's third-largest retailer, reported that its earnings rose 4.9 percent in the first quarter as the company embarked on a new marketing strategy to concentrate on apparel.

Sixteenth largest Dayton-Hudson, based in Minneapolis, reported net earnings of $22.6 million, or 47 cents per share, compared with $21.7 million, or 45 cents per share, in the first quarter last year.

The May Department Stores Co., 19th largest retailer and parent company of the Hecht Co., yesterday reported a 15.3 percent increase in first quarter sales.

Allied Stores, a New York-based company that is ranked 23d, said its net earnings for the quarter were $13.1 million, or 63 cents per share, compared with $2.4 million, or 12 cents a share, a year ago. Sales jumped to $761 million from $669 million in the first quarter last year.

K mart's first-quarter earnings were the second-highest for the period in the company's history, exceeded only by the first quarter of 1979 when it earned $45.6 million.

J.C. Penney Co. Inc. said that for the 13 weeks ended April 30, the company's income from continuing operations was $58 million (78 cents per share), up from $55 million (76 cents) in the year-earlier period.

Dayton Hudson earnings from continuing operations were up 31 percent to $21.7 million compared with $16.4 million in the 13 weeks ended May 1 last year. Sales rose 22 percent to $1.37 billion from $1.12 billion recorded in the first quarter last year.

St. Louis-based May Department Stores reported first-quarter sales of $846.8 million, compared with sales of $734.4 million last year.