Hello Jeffrey,
Congratulations on your new iPhone 5s! Also, thank you for the details of the issue you are experiencing with your purchased music
It sounds like you have tried the steps in the following article, and are not seeing your purchased music when looking in your Purchases:
Download past purchases
http://support.apple.com/kb/ht2519
If you are not finding your purchased music in Purchases, it may be that the music is hidden. Follow the steps below in iTunes on your computer to check if it is hidden and unhide it:
- Open iTunes on your Mac or PC.
- If you're not already signed in, choose Store > Sign in.
- Choose Store > View My Account. (You may be asked to enter your password again).
- On your Account Information summary, scroll down to the "iTunes in the Cloud" section and click Manage.
- Choose a content type by clicking Music, TV shows, Apps, or Books from the top.
- Click the Unhide button next to the item you would like to restore.
Note: If the item you are unhiding is not already downloaded on your computer locally, it will begin downloading automatically.
iTunes Store: Hiding and unhiding purchases
http://support.apple.com/kb/ht4919
If you are still not able to download the album, you can report the issue with this purchases using the steps in this article:
How to report an issue with your iTunes Store, App Store, Mac App Store, or iBookstore purchase
http://support.apple.com/kb/ht1933
Thank you for using Apple Support Communities.
Best,
Sheila M.