Backup to computer no worky w/storage issue

Have tried to backup iphone 5s to computer manually but says not enough disc space. Have freed up disc space and still no good. Have tried the icloud, bought extra storage for it and tried delesecting all apps/photos but the backup just seems to sit doing nothing (gives no estimated time). How can I backup so I can use my new iphone 6s+ ?? I can't to find any old backups either, which is strange, so I don't have a safety net. please help!