The Studio Theatre, one of Washington's new small professional groups, Thursday night opened its production of Peter Shaffer's "Five Finger Exercise" as its second offering, to run through July 15.

The Studio's premiere production was Lanford Wilson's "The Rimers of Eldritch," which drew serious critical notice.

"Five Finger Exercise," a play that turns on subtleties, will be a challenge to the new company.Shaffer, who also wrote "Equus" and "The Royal Hunt of the Sun," draws a portrait of an upper-middle-class British family that seems very comfortable and civilized until the arrival of a German tutor releases unexpressed frustrations and anxieties.

Studio Theatre shares space of 1443 Rhode Island Ave. NW with the Dance Exchange. The performances are at 8 p.m. Thursday through Sundays. For reservations, call 347-4700.

The Minority Arts Ensemble is looking for boys and girls between 8 and 18 years old for roles in its children's production, "Honey, I Love." The auditions will be held at All Souls Church, 16th and Harvard sts. NW, on Sunday, July 8, between 1 and 4 p.m. For appointments, call 398-3320.

Now in its eight season, Shakespeare & Co., which is based at the Trapier Theater on the grounds of the Washington Cathedral, will be opening "See How They Run," an English farce, on July 11.

Ted Walch is back once more as the artistic director of the company for a three-production summer season.

"See How They Run," which had a successful run on the London stage, is a good, clean farce about a zany day in an English vicarage and is offered as family entertainment.

The University of Maryland Theater Division again is offering summer classes in basic dramatics for children between 5 and 13 years old. The deadline for registration is July 16. For information, call 454-2541 or write: Creative Dramatics Classes, Division of Theater, University of Maryland, College Park, Md. 20742.

Two new one-act works combined under the joint title of "Power Plays" will close out the 1978-79 season for The New Playwrights' Theater.

The double bill will include a new comedy by Terry Paiste titled "Helen, Joan, and Half-Crazy Claire," and Mark Stein's play, rewritten after readings at the Phillips Woodrow Wilson's crusade to establish the league of Nations.

"Power Plays" opens on Friday, July 6, for previews and then will run through July 22 with Wednesday-through-Sunday performances.