It sounds like you are not able to locate some of your purchased songs on your iPod touch (5th generation) or iTunes on your computer.
First, I recommend checking to see if you are signed in with the Apple ID you used to purchase these songs under Settings>iTunes & App Stores on your iPod touch. If you are not signed in with the correct Apple ID, follow the steps in this article to change the signed in Apple ID:
Once you are signed in with the correct account, you can use the steps in this article to download the purchased music:
If you are still not able to locate the songs, you can report an issue with these purchases using the steps in this article: