The following comparison of various English versions might add to the conversation about the text of Hebrews 5:7:
Note that "fear" is not the only way it is translated. Other translations:
piety – NASB, Darby.
reverent submission – NIV, NRSV, Berean Literal Bible.
godly fear – NKJV, RSV, ASV, NWT.
reverence – ESV; CSB; Douay-Rheims 1899 American Edition (DRA); New American Bible (Revised Edition) (NABRE); Wycliffe Bible (WYC), 2001 by Terence P. Noble.
he feared – YLT, KJV/KJB, King James 2000, American King James, King James Bible: Purple Letter Edition, Webster Bible Translation, "Inspired Version of the Bible".
reverent fear – Jubilee Bible 2000; The Scriptures (ISR 1998) [Institute of Scripture Research].
he had God in reverence – Tyndale New Testament in Modern Spelling.
reverentia [in Latin] – Vulgate.
And some of these versions are pretty interesting:
and he was obeyed – Aramaic Bible in Plain English (also called The Original Aramaic New Testament in Plain English).
chasidus – Orthodox Jewish Bible (OJB), most of which is in English.
the terror from which he shrank – Weymouth.
He truly worshiped God.... – Contemporary English Version (CEV).
devotion – NET Bible.
devotion to God – Names of God Bible (NOG).
godliness – New Matthew Bible (NMB).
That's an amazing amount of variety!
So, was it fear, or something else?
The Greek at the end of Hebrews 5:7 says:
καὶ εἰσακουσθεὶς ἀπὸ τῆς εὐλαβείας – In a version of "Textus Receptus" (TR) and in the MGNT (Morphological Greek New Testament).
Note that there are a number of words in the Greek that are not translated into English; this might also mean something, but I am uncertain what at this time. Perhaps someone here might notice something about that.
Here is the text from the TR ("Textus Receptus"); and I believe the Morphological GNT matches it:
5:7 ὃς ἐν ταῖς ἡμέραις τῆς σαρκὸς αὐτοῦ δεήσεις τε καὶ ἱκετηρίας πρὸς τὸν δυνάμενον σῴζειν αὐτὸν ἐκ θανάτου μετὰ κραυγῆς ἰσχυρᾶς καὶ δακρύων προσενέγκας καὶ εἰσακουσθεὶς ἀπὸ τῆς εὐλαβείας.
One other thing, it is conceivable that verse 7 isn't in reference to Christ but to Melchizedek, like so:
 As [He] also says in another [place]:
"You [are] a priest forever
According to the order of Melchizedek."
 He, in the days of his flesh, when he had offered up prayers and supplications, with vehement cries and tears to Him who was able to save him from death, and was heard because of the godly fear/reverence/piety/devotion of his.
IF verse 7 is in reference to Melchizedek, which seems at least conceivable, then there is no theological difficulty.
On the other hand, there is a passage in the Isaiah that has been interpreted to be in reference to the coming Messiah, which passage says his delight will be in the fear of YHWH/YHVH (verse 3):
Isaiah 11:1-10 NKJV -
 There shall come forth a Rod from the stem of Jesse,
And a Branch shall grow out of his roots.
 The Spirit of the LORD shall rest upon Him,
The Spirit of wisdom and understanding,
The Spirit of counsel and might,
The Spirit of knowledge and of the fear of the LORD.
 His delight [is] in the fear of the LORD,
And He shall not judge by the sight of His eyes,
Nor decide by the hearing of His ears;
 But with righteousness He shall judge the poor,
And decide with equity for the meek of the earth;
He shall strike the earth with the rod of His mouth,
And with the breath of His lips He shall slay the wicked.
 Righteousness shall be the belt of His loins,
And faithfulness the belt of His waist.
 "†The wolf also shall dwell with the lamb,
The leopard shall lie down with the young goat,
The calf and the young lion and the fatling together;
And a little child shall lead them.
 The cow and the bear shall graze;
Their young ones shall lie down together;
And the lion shall eat straw like the ox.
 The nursing child shall play by the cobra's hole,
And the weaned child shall put his hand in the viper's den.
 They shall not hurt nor destroy in all My holy mountain,
For the earth shall be full of the knowledge of the LORD
As the waters cover the sea.
 "And in that day there shall be a Root of Jesse,
Who shall stand as a banner to the people;
For the Gentiles shall seek Him,
And His resting place shall be glorious."
† This quotation mark seems out of place. It was there at two different Websites.
The fear of YHWH/YHVH is a deep subject, as Psalms and Proverbs indicate:
Psalm 34:11 NASB -  Come, you children, listen to me; I will teach you the fear of the LORD.
And how about this "promise":
Psalm 34:9 NASB -  O fear the LORD, you His saints; For to those who fear Him there is no want*. *i.e., (great) lack.
Some of the passages that refer to significant results via the fear of YHWH/YHVH:
Psalm 19:9a NASB - The fear of the LORD is clean, enduring forever; ...
Psalm 111:10a NASB - The fear of the LORD is the beginning of wisdom; ...
Proverbs 1:7 NASB - The fear of the LORD is the beginning of knowledge; Fools despise wisdom and instruction.
Proverbs 8:13 NASB - "The fear of the LORD is to hate evil; Pride and arrogance and the evil way And the perverted mouth, I hate.
Proverbs 9:10 NASB - The fear of the LORD is the beginning of wisdom, And the knowledge of the Holy One is understanding.
Proverbs 14:27 NASB - The fear of the LORD is a fountain of life, That one may avoid the snares of death.
Proverbs 15:33 NASB - The fear of the LORD is the instruction for wisdom, And before honor [comes] humility.
Isaiah 33:6 NASB - And He will be the stability of your times, A wealth of salvation, wisdom and knowledge; The fear of the LORD is his treasure.
Isaiah 33:6 NIV - He will be the sure foundation for your times, a rich store of salvation and wisdom and knowledge; the fear of the LORD is the key to this treasure.
Other interesting tidbits:
Near the end of Ecclesiastes:
Ecclesiastes 12:13 - The end/conclusion of the matter, after all has been heard: Fear elohiym, and keep his commandments: for this [is] the whole of Man.
Job 33:12-13a -  "Look, in this you are not right. I answer you, for elohiym is greater than Man.  Why do you contend against him...?
And an interesting one, just a tad out of context:
Deuteronomy 14:23 - "You shall eat in the presence of YHWH your elohiym... so that you may learn to fear YHWH your elohiym always.
- "fear of the LORD" occurs 25 times in 25 verses in the NASB.
- "fear God" occurs 18 times in 18 verses in the NASB.
- "fear the god" occurs 1 times in 1 verses in the NKJV, but not in the NASB.
- "fear of Jesus" occurs 0 times in 0 verses in the NASB.
- "fear Jesus" occurs 0 times in 0 verses in the NASB.
- "fear of the Christ" occurs 0 times in 0 verses in the NASB.
- "fear of Christ" occurs 1 times in 1 verses in the NASB.