How to restore my pictures after my iphone 4 was stolen, to my iphone 5?

My phone was stolen on 13th of August last year. I had an iPhone 4. I never found my phone again so I got an iPhone 5 (which I now have).
I was wondering if I could restore my pictures that were on the old iphone. Any help would be greatly appreciated!
I know you can't backup a newer version to an older version of iPhone, but I was wondering if I could do it from iPhone 4 to 5?

Thank you in advanced for all of your help.

Added (1). Update: I do had my pictures saved on iCloud, I just didn't have sharing stream on, so I understand I can only restore the pictures on an iOS device and not in an actual PC/laptop. However, I don't really know how to do it. I only know how to restore whatever has been backed up in my actual phone.

If you have the photos on icloud then you can get them back. If not then i'm sorry

If you backed it up on iCloud then you can just plug your new phone in the computer and back it up and all your photos will be there.

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