Q: Why can I only hear about 5 of the 68 songs I have on my iPod shuffle?

Select the shuffle in iTunes (click its device button on horizontal bar) to show its settings screen in iTunes window.  Along left side (in the sidebar), under On My Device, click Music.  To the right, the shuffle's song list (songs currently loaded on the shuffle) is shown.  Does it show about 5 songs, or 68?

If it's about 5 songs, that's why you only hear about 5 songs when playing the shuffle.  The solution is to properly load the remaining songs.  If you see 68 songs, the solution is to understand why the other songs are not playing.  Please post back with your findings.

In your iTunes music library, compare the about 5 songs that DO play (on a plain song list with columns).  You can put them on a playlist, to make it easier to compare them, and show it using the Songs view.  Show the columns for Bit Rate and Kind (right-click column heading to show/hide columns).  What (if anything) do they have in common? 

Do the same thing for the remaining songs that do NOT play.  What (if anything) do they have in common?

When you say "resetting," is that a Restore?

Use iTunes on your Mac or PC to restore your iPhone, iPad, or iPod to factory settings - Apple Support

Did you do a Restore, following the procedure in link from previous reply?

Does you complete iTunes music library fit on your iPod shuffle, or will you be syncing only a portion of it to your iPod shuffle?