Q: how do i recover deleted voicemail from my Iphone 5

Have you looked in the Deleted Messages Folder?

The message(s) should be there until you select Clear All

Have you tried to recover them from your iCloud backup file? You may have a try.

Another way is to scan your iPhone 5 with a third party easy iphone recovery utility to check whether it can find the deleted voice mail messaga.

Though this is an old post, hope this answer is helpful for people with the same problem.