Need to restore a backup from iphone 5 to iphone 4, help please!

iPhone 5: iOS7 latest update (I'm fairly certain)
iPhone 4: 7.03, 13.5 GB capacity, 12.6GB available
MacBook Pro: OSX 10.8.5
My iPhone 5 was stolen last night. I've been backing it up pretty regularly, but almost exclusively to iCloud (I now realize I should have been backing it up to my computer and iCloud regularly...). I have an old regular iPhone 4, that I downloaded iOS7 to, but I'm having trouble restoring any iPhone 5 backups to my old iPhone. I restored my iPhone 4 to factory settings then downloaded iOS 7 to my iPhone 4 and am given the option to restore the last backup of the iPhone 4 (from MONTHS ago) to this device, but cannot find the option to restore my iPhone 5 backups??? My last backup to my iphone 5 is large (a little over 11.6 GB), but still smaller than my iPhone 4 capacity...
How can I restore my last iPhone5 backup to my iPhone 4? Can I partially restore from iCloud (i've been reading that this would have been easier if I had backed up directly to my macbook)? What programs can I use to do this?
ANY HELP WOULD BE GREATLY APPRECIATED! I don't need everything that was lost on that phone (I had TOO many photos) but certain messaging conversations and notes I definitely need.
Please let me know if you can help but need more info!
THANKS!

Sorry for being unclear :S
I erased my iPhone and went through the set up and tried to restore to iCloud but didn't get the option to restore to my iPhone 5 backup (only iPhone 4 backups--I assumed because erasing my phone and going to factory settings meant back to iOS6) so I went through with just factory settings. (I did all of this on my phone, not on my computer/iTunes as my backups are saved onto iCloud) I then signed into my iCloud account on my phone and went to Settings>iCloud>Storage & Backup>Manage Storage then I can see the following
If I click on my iPhone5 (the first one) I see this
I can delete the backup, but how do I restore it to that last backup from yesterday??

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