Securities offerings by law companies during the first five months of 1981 more than tripled in both number and dollar value from the same period last year, according to figures compiled by the Securities and Exchange Commission.

During the same period, bond offerings declined by almost a third, from $21.8 billion to $15.2 billion, with corporation holding back from trying to raise cash in a market badly depressed by high interest rates.

All in all, total proceeds to companies who issued securities offerings -- stocks or bonds -- were down by $4.1 billion or 13 percent, with the dismal bond market accounting for most of that decline. They were $28.6 billion compared with $32.7 billion for the same period in 1980.

New issues -- stock in companies that previously had not registered stock offerings with the SEC -- provided what buoyance there was, according to the SEC. They increased to 224 from 65 in number and to $1,53l million from $432 million in 1981 from 1980.

"It's a healthy sign," said Jeffrey Schaefer, senior vice president and director of research for the Securities Industry Association. "It's been rebuilding since the second half of 1978," he said. Then a change in the maximum rate of capital gains taxes from 49 percent to 28 percent made such investments more attractive, he said.

Because new issues are often speculative in nature, investors generally expect to take their profits in capital gains over the short run rather than depending on steady income from dividends. The change in capital gains combined with an impressive performance by the newcomers has made new issues an attractive investment, Schaefer said.

The SIA's research shows new issues performing better than large company indexes, Schaefer said. "Raising money from the public is much easier" as a result, he said.