Set the architecture in build setting to Standard architectures(armv7,armv7s)
iPhone 5S is powered by A7 64bit processor. From apple docs
Xcode can build your app with both 32-bit and 64-bit binaries included. This combined binary requires a minimum deployment target of iOS 7 or later.
Note: A future version of Xcode will let you create a single app that supports the 32-bit runtime on iOS 6 and later, and that supports the 64-bit runtime on iOS 7.
From the documentation what i understood is
Update (Xcode 5.0.1)
In Xcode 5.0.1 they added the support to create 64 bit binary for iOS 5.1.1 onwards.
Xcode 5.0.1 can build your app with both 32-bit and 64-bit binaries included. This combined binary requires a minimum deployment target of iOS 5.1.1 or later. The 64-bit binary runs only on 64-bit devices running iOS 7.0.3 and later.
Update (Xcode 5.1)
Xcode 5.1 made significant change in the architecture section. This answer will be a followup for you.
Check this