Before trying anything else, if you have not already, power off the iPod touch (press-hold the power button and "slide"). After starting it up, see if the problem still occurs.
The key here may be to figure out why those "5 songs" have no problem playing, while all of the other do not play. If your songs are purchased from the iTunes Store, are the "5 songs" your most recent purchases? Or were they purchased from iTunes Store on the iPod touch, versus being synced to the iPod from your computer for all other songs?
Did you recently start using a different Apple ID? Is the Apple ID used on iPod touch different from the Apple ID used in iTunes on the computer?
Do you (or did you) subscribe to Apple Music (or iTunes Match)?
What iOS version does your iPod touch run?