Use an iPhone 5 Nano-SIM in an iPhone 4?
There are a number of Nano-SIM to Micro-SIM adaptors on the market that will let you drop your iPhone 5's Nano-SIM card in to your iPhone 4. Not only would this bring along any data you had saved on the Nano-SIM, but you'd get your phone number from the iPhone 5 would presumably be assigned to the iPhone 4 assuming all things were equal and the phones were on the same carrier network. Once in your iPhone 4, you could copy the data off the SIM on the phone's internal storage.

I don't want to link to specific purchase sites for these things since that kind of information. But here's a search query that'll turn up many options: https://www.google.com/q=nano+sim+to+micro+sim+adapter