I don't see the value in any such a book but, assuming you do, the issue is NOT whether your publication of the book would be a "fair use," but rather whether your publication of each one of the song snippets, on an individual basis, would be fair.
If, for example, you published the snippet "Why don't we do it in the road" and properly attributed the line to John Lennon and Paul McCartney, your publication would likely NOT be fair because that line is [with one exception] the only lyric in their "Why Don't We Do It In The Road" song.
A more difficult question would be if you published the snippet "Take these broken wings and learn to fly" from Lennon and McCartney's song Blackbird. While that line is one of a handful comprising the lyrics, it encapsulates the meaning -- indeed the very purpose -- of the song. In copyright lingo, that line just may be the "heart" of their work.
An easy case going the other way would be if you published the snippet "The wild and windy night" from the Lennon and McCartney song The Long and Winding Road. That snippet is one of many comprising the lyrics and, in isolation, has no meaning beyond the words themselves. Your publication of that snippet would be "fair."
I think you'll find that the book you envision publishing could only lawfully publish snippets from songs if the snippets are bland and meaningless. Even if, however, you could lawfully publish snippets with meaning [such as "Take these broken wings and learn to fly"] I frankly do not see much value in the book. But to each his own.
If you proceed, you NEED to discuss your plans with an experienced copyright attorney. Good luck.
Generally short quotes aren't copyrightable, and 5-20 words is very short, but the problem is that these quotes, if from songs, are already copyrighted, and are owned by the songwriters' music publishers, each of whom would require their permission for you to quote their works.
Even if you're able to get permission, you can't use any musician's image if you don't properly license it, or anyone's name, image, or trademark to market the book.
Disclaimer: Please note that this answer does not constitute legal advice, and should not be relied on, since each state has different laws, each situation is fact specific, and it is impossible to evaluate a legal problem without a comprehensive consultation and review of all the facts and documents at issue. This answer does not create an attorney-client relationship.
You are asking, in effect, whether your book would fall under the "fair use" defense to copyright infringement.
It is impossible to answer your question without more information - and, even with more information, it may be difficult to provide a definitive answer.
The post at the link below discusses the four factors that, at a minimum, must be considered in any fair use analysis. If this issue is important enough, you should retain an attorney to analyze all of the facts and provide an opinion.
Disclaimer: This post does not constitute legal advice and does not establish an attorney-client relationship.