National Savings and Trust Co., the fifth-largest commercial bank, in Washington, yesterday reported record 1977 profits.

Not counting gains or losses from selling securities, NS&T earned $2.97 million (16.49 a share) compared with $2.2 million ($4.82) the previous year.

After securities gains, per sharing earnings were up 34.6 per cent to $6.49 compared with $4.83 in 1978.

Chairman Douglas R. Smith said assets rose to a record $373 million on Dec. 31 from $330 million a year earlier. Deposits rose to $340.6 million from $298.9 million.

Directors, meantime, approved an increased quarterly dividend of 65 cents a share on its common stock, payable Feb. 1 to stockholders of record Jan. 20. Previously, NS&T pad 60 cents a share quarterly.

Virginia National Bankshares, a Norfolk-based bank holding company, soon will report 1977 per share earnings of a record $3.18, up 14.4 per cent over $2.74 earned in 1976, when net income was $12.3 million.

VNG chairman W. Wright Harrison disclosed the figures yesterday in a talk with securities analysts. Although he gave no other figures, the 1977 per share earnings reported would be 6 per cent high than the previous record.

American Health Services, Inc., reported earnings in the year ended Sept. 30 rose to $853.953 ($1 a share) compared with $700,463 (82 cents) the previous year, a gain of 22 per cent. Sales rose to a record $20 million from $17 million.

The Washington-based company owns, operates or manages 10 psychiatric or general hospitals and nursing homes.