Now if I got in Shrink by file I get some strange data saying currently allocated space of 1300 MB and 82.81 MB free.
Ok if I go into Shrink for the log file it shows a 31733.63 MB currently allocated and 26354.71 MB free.
Ah, now things make sense. You've got a very small amount of data (1.3GB) but a massive log file. Backups don't contain the entire transaction log. They just need enough of the log to recover the database once restored. That large backup must have occurred when there was a huge uncommitted transaction, or lots of unreplicated transactions and hence it needed to backup most of the log. The more recent backup didn't.
You might want to investigate and see why a 1.3 GB database has 5 GB of log in use. Large transactions, replication falling behind, lack of log maintenance?
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: Discussions on DB performance with occasional diversions into recoverability
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