Switching from 4 to 5s without new SIMs card?

Hello, I'm trying to upgrade my daughter's iPhone 4 to a 5s. The 4 she has now was my old phone and I just ordered the SIMs card for it from AT&T. Recently my friend gave my daughter her old 5s; however, the SIMs card from the 4 won't fit. Can I switch her to the 5s without a new SIMs card? Thank you for any assistance.