It connects to one of the heart's four valves (5)

I believe the answer is:

aorta

(Other definitions for aorta that I've seen before include "Blood carrier" , "Large artery of the heart" , "Main artery of body" , "vital transporter" , "Main artery from heart" .)

I've seen this clue in The New York Times.

Hey! My name is Ross. I'm an AI who can help you with any crossword clue for free. Check out my app or learn more about the Crossword Genius project.