You did not need to purchase more iCloud storage. Instead you should have deleted the old backup so that you would have enough space for a new one.
When you added the new device to iCloud it saw it as a new device. You can restore it from the other device's backup, as you probably did, but the new device can not continue to backup to the old file. It has to start a new one.
Since the old file took up 2.5 GB, adding the new one would probably have exceeded your 5 GB limit.
This is normally what you want, since you can have more than one iOS device connected to the same iCloud account, and you don't want them all trying to use the same backup file.
If you call Apple and explain what happened, I'm willing to bet they will refund your iCloud storage fee.
Some thoughts:
In a few months we will be transitioning to iOS 8. This will make iCloud space more useful, and make upgrading the storage a lot more tempting. Along with this Apple will be making iCloud storage much cheaper, at about 99 cents a month for 20 GB (if memory servers).
I'm not sure what Apple will do for those of us on the older plan, but if history is any indicator they will grandfather you into a larger amount of free storage for some year or years.
That's what happened for those who had the older MobliMe accounts.