Jack said there was a dog that was a high flying, nineteenth century trapeze artist; his clam is intriguing, yet highly unlikely. What is the correct way to use hyphens in this sentence

Jack said there was a dog that was a high-flying, nineteenth-century trapeze artist; his claim is intriguing, yet highly unlikely.

Explanation:

Hyphens are used when there is a need to form a compound adjective that comes before a noun. This enables the compound adjective to modify or describe the noun that follows. But when the compound adjective comes after a noun, then there is no need to hyphenate the word.

In the given sentence, the words "high flying" and "nineteenth century" are used to describe the word "artist" which is a noun. Therefore, they are hyphenated to make a compound adjective and help describe the artist dog,

Thus, the final sentence will  be written as-

Jack said there was a dog that was a high-flying, nineteenth-century trapeze artist; his claim is intriguing, yet highly unlikely.

not going to be don't need a Bf.