Q: Itunes is not syncing music to my ipod 5th Generation.

To use automatic syncing to load music on an iPod, you need to set up the iPod's Music tab in iTunes.

Select the iPod in iTunes.  There is a row of "tabs" (starting with Summary). Click on Music there.  If the iPod is currently set up for automatic syncing, Sync Music should be checkmarked there.  Below that, if your entire iTunes Music library will fit on the iPod, you can choose to sync Entire music library. 

Otherwise, you can choose to sync Selected playlists, artists, albums, and genres.  Below that, create a selection of songs that you want synced to the iPod.  Those recently downloaded songs need to be included in the selection, if you want them to sync to the iPod. 

When you Apply the change, the selection of songs on the Music tab syncs to the iPod.  Going forward, any changes you make to your iTunes Music library, that are related to the selection on the Music tab, sync automatically the next time you connect the iPod (or click the Sync button).

NOTE:  If Sync Music was not already checked on the Music tab, when you click Apply, the iPod's current content will be replaced by the selection of songs on the Music tab.

Here is one simple way to set it up.  Create a new regular playlist in iTunes and call it something like "iPod Songs."  Put ALL of the songs you want on the iPod on that playlist, including those recently downloaded songs.  On the iPod's Music tab, select ONLY that new playlist as your selection.  When you click Apply, the songs on that playlist sync to the iPod. 

Going forward, when you want to update the songs on the iPod, just update that playlist (add and remove songs).  The next time you connect the iPod (or click the Sync button), iTunes updates your iPod with your changes.