Hebrews 5:7 says God heard Him, but you need to continue reading to Hebrews 6:6, then read Hebrews 9 & 10 which clearly shows that the Lord Jesus Christ was crucified and died.

The Apostle Paul preached that the Lord Jesus Christ was crucified, died and resurrected.

1 Corinthians 1:23
but we preach Christ crucified

Galatians 2:20
I have been crucified with Christ. It is no longer I who live, but Christ who lives in me. And the life I now live in the flesh I live by faith in the Son of God, who loved me and gave himself for me.

So Hebrews 5:7 is just saying that God heard His supplications but not to stop Him from being crucified and dying, but to make Him the author of eternal salvation to all who obey Him

Jesus said he would die.

Matthew 16:21 From that time forth began Jesus to shew unto his disciples, how that he must go unto Jerusalem, and suffer many things of the elders and chief priests and scribes, and be killed, and be raised again the third day.

For even the Son of Man came not to be served but to serve, and to give his life as a ransom for many.”
Mark 10:45

for this is my blood of the covenant, which is poured out for many for the forgiveness of sins.
Matthew 26:28

After his resurrection and ascension he said he had died.

Revelation 1:18
I am he that liveth, and was dead; and, behold, I am alive for evermore, Amen; and have the keys of hell and of death.

Jesus did not only pray for the cup of suffering to pass, but also that God’s will to be done. Hebrews confirms this fact also in the following chapters;

Hebrews 7.27
Unlike those other high priests, he does not need to offer sacrifices every day. They did this for their own sins first and then for the sins of the people. But Jesus did this once for all when he offered himself as the sacrifice for the people’s sins.

Hebrews 9:12,14-15,26-28
[12]With his own blood—not the blood of goats and calves—he entered the Most Holy Place once for all time and secured our redemption forever.
[14]Just think how much more the blood of Christ will purify our consciences from sinful deeds so that we can worship the living God. For by the power of the eternal Spirit, Christ offered himself to God as a perfect sacrifice for our sins.
[15]That is why he is the one who mediates a new covenant between God and people, so that all who are called can receive the eternal inheritance God has promised them. For Christ died to set them free from the penalty of the sins they had committed under that first covenant.
[26]If that had been necessary, Christ would have had to die again and again, ever since the world began. But now, once for all time, he has appeared at the end of the age to remove sin by his own death as a sacrifice.
[27]And just as each person is destined to die once and after that comes judgment,
[28]so also Christ was offered once for all time as a sacrifice to take away the sins of many people. He will come again, not to deal with our sins, but to bring salvation to all who are eagerly waiting for him.