Hebrews 5:9 says ‘and, once made perfect, he became the source of eternal salvation for all who obey him.’ Is the word obey referring to all who believe in the Gospel or some other kind of obedience?
In the New Testament unbelief is sometimes equated with disobedience. The word translated obey here actually means to listen, as to a call.
God has made Himself so obvious to us that He sees the failure to believe in Him as an act of disobedience. Since being a just God means He has to see that everyone will receive at least one bonafide offer of pardon during his or her lifetime, refusing to listen to this offer and respond is like refusing to obey.
Regarding our salvation, passages like John 3:16, John 6:28-29, and John 6:40 and others make it clear that belief in the Son is what the Father requires of us for salvation.