"During His earthly life, He offered prayers and appeals with loud cries and tears to the One who was able to save Him from death, and He was heard because of His reverence." Hebrews 5:7
As with most Muslim assertions, this is another verse which they have to wrench out of its context to support a claim which has neither historical nor doctrinal Biblical support. Neither does it find any support in secular history.
But Hebrews is one of the worst of the Books of the Bible to choose for making this claim, as it is chockfull of information that belies the allegation that Jesus never died on the cross. This is one of the most easily disproven of Islam's errors.
Any reader of the Book of Hebrews will find that it teaches at some length on the High Priesthood of the Messiah, Jesus. Those familiar with the Torah know that it was YHWH Who instructed Moses to ordain a Levitical priesthood, beginning with Aaron as the first High Priest. The High Priest was the only Israelite who could go into God's Holy of holies inside the Jewish Temple to make a sacrifice on behalf of the Jews and all nations. And this, just once a year on the Day of Atonement.
It was that very blood sacrifice which Yahweh said would atone for the sins of man. But Jesus' High Priesthood far exceeded that of ordinary men. This because He was not just our High Priest, but He was also the Perfect Sacrifice Who would fulfill the Law. As Yeshua -- Jesus, the Messiah -- told His people (italics mine for emphasis),
17 “Don’t think that I have come to abolish the Torah or the Prophets. I have come not to abolish but to complete.
18 Yes indeed! I tell you that until heaven and earth pass away, not so much as a yud or a stroke will pass from the Torah — not until everything that must happen has happened." Matthew 5 (Complete Jewish Bible)
And what were those things that first needed to happen?
After more than 3 years of preaching, Jesus began to repeatedly teach His disciples that He would be arrested, abused and then killed by the religious leaders, but that He would rise again after three days. At the Last Supper they had together before His death, He told them that His would be the ultimate sacrifice for the sins of mankind:
27 Then He took a cup, and after giving thanks, He gave it to them and said, “Drink from it, all of you.
28 For this is My blood that establishes the covenant; it is shed for many for the forgiveness of sins." Matthew 26
Just hours later, He was dead. But, just as He promised, after three days He rose again from the grave and appeared to His followers. Forty days after that, He returned to heaven from whence He had come. His mission had been accomplished, the Law had been perfectly completed, as the CJB (Complete Jewish Bible) puts it.
That is the background of the entire Book of Hebrews. The author of the Book is well aware that Jesus died because "Jesus as High Priest and Perfect Sacrifice" was the point he was making to his audience: the Hebrews. People who would have been quite familiar with the yearly Passover and Day of Atonement rituals instituted and observed by Jews for more than a millennium and a half prior. The point might have been entirely lost on a 7th century Arab trader who proved quite ignorant of the Bible's teachings, but it was most certainly not lost on these Jews of the First and succeeding centuries.
The Book also contains many verses which speak of Jesus' sacrificial death. At the very beginning of the Book, in just the 3rd verse of the first chapter, we are already told that Jesus died and fulfilled His role as the Lamb of God and High Priest (italics mine):
3 The Son is the radiance of God’s glory and the exact expression of His nature, sustaining all things by His powerful word. After making purification for sins, He sat down at the right hand of the Majesty on high. Hebrews 1
Sans a spotless sacrifice, there would have been no such purification for sins. Jesus' resurrection was proof that the Father had accepted the Sacrifice and Jesus' sitting at His right hand completes the picture of the Messiah's success at His mission.
As we said earlier, all one needs to do is read through the rest of the Book of Hebrews to find the author stating quite clearly that Jesus died. Here are a few examples (italics mine for emphasis. Text in brackets mine):
Hebrews 2:9 But we do see Jesus—made lower than the angels for a short time so that by God’s grace He might taste death for everyone—crowned with glory and honor because of His suffering in death.
Hebrews 2:14 Now since the children have flesh and blood in common, Jesus also shared in these, so that through His death He might destroy the one holding the power of death—that is, the Devil—
Hebrews 6:6 and who have fallen away, because, to their own harm, they are recrucifying the Son of God and holding Him up to contempt. [One cannot recrucify someone who has never been crucified. This says that Jesus was crucified and that He did die]
Hebrews 7:27 [Jesus] doesn’t need to offer sacrifices every day, as high priests do—first for their own sins, then for those of the people. He did this once for all when He offered Himself. [Offering Himself as a sacrifice means He died]
Hebrews 9:11 But the Messiah has appeared, high priest of the good things that have come. In the greater and more perfect tabernacle not made with hands (that is, not of this creation),
12 He entered the most holy place once for all, not by the blood of goats and calves, but by His own blood, having obtained eternal redemption.
13 For if the blood of goats and bulls and the ashes of a young cow, sprinkling those who are defiled, sanctify for the purification of the flesh,
14 how much more will the blood of the Messiah, who through the eternal Spirit offered Himself without blemish to God, cleanse our consciences from dead works to serve the living God?
Who is the God of the Book of Hebrews?
Jesus Teaches About His Coming Death and Resurrection