Option(E) is correct
A modifying phrase needs to be placed by the word it modifies. However, in the original sentence, the modifying phrase written in Austria in 1762 incorrectly modifies the composer. It makes no sense that the composer was written in Austria. Instead, Symphony No. 5 was Written in Austria in 1762.
The subject pronoun who needs to be replaced by the object pronoun whom since Haydn is not the subject of the sentence. Rather, many [individuals] later called is the subject and they are calling Haydn, who is the object, an important musician.
A. Written in Austria in 1762 illogically modifies a composer, not a composition; the subject pronoun who is used instead of the object pronoun whom
B. The pronoun who illogically refers back to Symphony No. 5
C. The subject pronoun who is used instead of the object pronoun whom
D. Written in Austria in 1762 illogically modifies a composer, not a composition
E. Written in Austria in 1762 correctly modifies a composition (Symphony No. 5, not its composer); the object pronoun whom is correctly used instead of the subject pronoun who