The most common and most likely answer to this crossword clue is the 5 letter word IBSEN
I
B
S
E
N
More clues leading to the result IBSEN
- One book by Sterne? Oddly, a different writer
- Dramatist is brilliant, so educational — Norwegian originally
- One heading for snow protected by mountain is a famousNorwegian
- Dramatist whiNES BIography is holding him up
- Dramatist elevated in Verlaine's biography
- Writer's current book dispatched without back cover
- Stock complaint received by popular playwright
- Playwright identified by some lines bitterly upset
- Children's author briefly raised dramatist
- Some aeroplanes Biggles sent up for playfellow
Buddy explains!

The straight part
We know that "Playwright" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case playwright = ibsen.The cryptic/wordplay part
In cryptic crossword there's often an wordplay/cryptic part as well.This part involves a more complex hint, such as an anagram, homophone, hidden word, etc.
Sadly, We don't have an explanation for this specific crossword clue yet.