Ditch your old phone backups
First, get rid of old phone backups you no longer need. Go to Settings > General > Storage & iCloud Usage, and tap Manage Storage under the iCloud section. If there are any device(s) you no longer own or use listed there, tap 'em and click "Delete Backup." There's no reason to let whatever crap was on your iPhone 4 hog up your precious 5GB of free iCloud space.
Now before we move on to the next part, and especially if your current phone hasn't been backed up in a while (or ever), plug it into your computer and do a backup via iTunes (File > Devices > Back up). You'll also want to transfer your photos and videos on to your computer as well.