How can I retrieve the deleted backup file from iTunes for iPhone?
Usually the backups are stored in this location:


  ~/Library/Application Support/MobileSync/Backup/


Just hop into TimeMachine or whatever your backup solution is and restore the contents of that folder.  



Digging into these files is hit or miss and based on the version of iTunes and encryption settings, they may only be understood by iTunes. There is no easy way to get specific info (like contacts or calendars) from these files. Besides the name of the files are random numbers and letters, so good luck making sense of that...

As to the initial dilemma, I don't really understand what happened. iTunes never deleted a backup, unless I did it manually in the Preferences. Do you see some backup files in iTunes Preferences > Devices, especially ones dating before the upgrade to iOS 5? I find it very odd that in the middle of the upgrade it would decide to destroy such important data.

Do you have a Time Machine backup? Were you subscribing to a sync service like MobileMe, or Google where your contacts and other stuff like that would still be?

And how did you delete the backup files actually? Did you do it manually or the OS asked your permission to do it?