My iPhone 5 has an iTunes logo?

I tried to update my phone to ios7 and in the middle of the update my computer froze. Now I have the logo that is saying to plug it into iTunes. I do that and no computer recognizes it. I have tried DFU and other methods and nothing has worked.

A computer with the latest iTunes is recommended because previous versions may not recognize the latter versions of iOS.

If not, then try to do a hard reset on you handset, then try again. But make sure your iTunes has sycned all the apps and so on from iPhone to iTunes.