Can I put iPhone 5 sim in iPhone 4?

I broke my phone, and if I can't do that I'm screwed

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.

Very warmfu

You'd need either an adapter or get your carrier to issue a microSIM with your number on it.

iPhone 4 - microSIM
iPhone 5 - nanoSIM

You'll need a nano-SIM to micro-SIM adapter so you can use your nano-SIM in your iPhone 4 which takes micro-SIM. You can get that from any cellphone store.