Cannot restore my back up on iphone

[taylorwilliamallen]

I have a unique problem, i backed up my 5s to my laptop which was running the older ios, i then lost it and purchased a 5c to get me by until my upgrade. when i plugged the iphone 5c in it told me i needed to upgrade it before it could be restored. i did this but then i was told i had to download the newest version of itunes to run that iphone. i downloaded the newest itunes which then told me i couldnt run it because i dont have a new enough version of windows. so i downloaded the older version of itunes but it will not recognise my iphone because it has the newest update so is there anyway i can get the back up from my laptop onto icloud or another software to then download onto my iphone?