According to this matter, here are two solutions:
Part 1:Recover Deleted Contacts from iPhone 5/4S without Backup
Currently, this iPhone Data Recovery can directly scan iPhone 5 and 4S to recover lost contacts directly. Here are the steps.
Step 1.Connect your iPhone 5/4S to the software
Firstly, download the proper version of iPhone Data Recovery and install it to your computer, run it.
Step 2.Scan the iPhone
After your iPhone is connected to the software, hit Start Scan to scan the lost contacts on your iPhone.
Step 3.Preview and recover deleted contacts from iPhone 5/4S
After the scanning is completed, you will see all data found on your iPhone are categoried in the left panel.
Part 2: Restore iPhone Contacts by Extractring from iTunes Backup
A:Select recovery mode
First, select Recover From iTunes Backup File mode after you ran this iPhone Contacts Recovery software.
B:Preview and recover lost contacts from iTunes backup
After the scan, all data found in the backup will be listed in the left panel. Go to the Contacts folder to preview the detailed contacts, and mark the ones you need, hit Recover button at last to save the contacts to your computer.