Looks like this is a known issue. From the Xcode 5 release notes:

After switching the minimum deployment target of an application from iOS 7.0 to a release prior to iOS 7.0, building and running the application may fail with the message "iOS Simulator failed to install the application."

• Go to the iOS home screen, click and hold the application icon, then tap the hovering "X" button to delete the application. 13917023

Another release note:

iOS Simulator

• If an iOS app is detached, relaunching the same app from Xcode will result in a black screen in the Simulator even though the new app is launched. Terminate the app in the Simulator or relaunch it for the second time. 14648784