Alas, no.
QUIDCO have some terms and conditions on their Apple page....
"Cashback is not available on the iPhone 5S/5C."
Why must everyone hate on Apple! I know this sounds silly, but whenever a new Apple device comes out, everyone ups their prices or denies offers. The opposite thing happens is Samsung, or anything non-apple branded. I believe Quidco were even promoting it with their cash back offer when it came out!