Could the songs of Revelation 5 and 14 be the same?
Answer: It seems that they are not — but there may be much more to this question.
This is a fascinating subject because of its implications. Suppose we first contrast the two verses as with the OP:
Revelation 5:8-9: "When [the Lamb] had taken the book, the four living creatures and the twenty-four elders fell down before the Lamb... And they sang a new song, saying, “Worthy are You to take the book and to break its seals; for You were slain, and purchased for God with Your blood men from every tribe and tongue and people and nation.
As has already been observed by @Dottard this appears to be more of a hymn than a song, per se. Then we have:
Revelation 14:1-3: Then I looked, and behold, the Lamb was standing on Mount Zion, and with Him one hundred and forty-four thousand… 2And I heard a voice from heaven, like the sound of many waters... 3And [the harpists playing on their harps] sang a new song before the throne and before the four living creatures and the elders; and no one could learn the song except the one hundred and forty-four thousand who had been purchased from the earth*" (emphasis added).
Since "no one could learn the song except the 144,000, it seems clear that this is not the same as that which the 24 elders sang, since they "could not learn it." The "songs" do not appear to be the same.
But let us try to understand what this may be communicating.
I. Who are the 144,000? They are "[those] who have been purchased from the earth." And, just who are they, precisely? Well, 144,000 is a special number in that it is: 122 * 103, a number representing completeness — the full compliment of the N/T faithful. Those who "have been purchased" must surely be the saints, all saved by the blood of the Lamb.
II. How do we differentiate between the first group in Revelation 5 with the second group in Revelation 14?
Well, the first group consists of at least the "24 elders." While many (including me) have felt that these are merely a combination of the 12 tribes of Israel and the 12 apostles, perhaps that is not quite correct.
Suppose the "24 elders" actually represent all the faithful of the O/T only (of course, that doesn't explain the addition of "the four living creatures"1).
There seems to be very little wiggle-room that the 144,000 are New Testament Christians. And, in that case, they would naturally sing a different song than those of the Old Covenant whose "song" was the "Song of Moses." It therefore stands to reason that the "song" the 144,000 are singing may, in fact, be the Gospel: the N/T itself. This might be considered "the song of Christ" that only the saints would (or could) know.
This is a symbolic interpretation of the two "songs" and why they appear to differ.
[Note: No doubt there will be those who disagree. They may reject this analysis entirely. But the 144,000, and their song, appears at the very least to be the full compliment of the saved in Christ, singing the "song" of salvation in His Name, something that had yet to be revealed to the O/T faithful, perhaps represented by the 24 elders. The Book of Revelation can indeed be a great challenge.]
1 I have believed that the "four living creatures" may be representative of the four Gospels. The creatures from Ezekiel 10 were described as having 4 faces: a lion, an ox, a man, and an eagle. If this is true, the lion ("lion of Judah") would represented by Matthew's Gospel, the ox ("servant") by Mark's Gospel, the man ("Christ's humanity") by Luke's Gospel, and the eagle ("flying in the heavens") by John — where Christ is God.