Hello jonnycakes15,
Thank you for the details of the issue you are experiencing with the Remote app on your iPhone 5S. If you have a current version of iTunes, you do not need to enter a 4 digit code. With iTunes 10.0.1 or later, your identity will be verified by signing into Home Sharing with the same Apple ID on both devices:
Setting up Remote app
Remote app 2.0 or later uses Home Sharing for setup and control with iTunes 10.0.1 and/or Apple TV (2nd and 3rd generation).
iTunes (10.0.1 or later)
- Open iTunes on your Mac or PC.
- iTunes 11 or newer: Turn on Home Sharing in iTunes by going to File > Home Sharing> Turn on Home Sharing.
iTunes 10.7 or older: Turn on Home Sharing in iTunes by going to Advanced > Turn on Home Sharing.
- Connect iPhone, iPad or iPod touch to a Wi-Fi network that is connected to the local network that your Mac or PC is also connected to.
- Open the Remote app (software version 2.0 or later) on your mobile device.
- Turn on Home Sharing in the Remote Settings screen. Make sure to sign into the same Home Sharing account you used to sign in to from iTunes on your computer.
Once Home sharing is enabled for both your computer and your mobile device, Remote app will be be able to view and control audio and video playback in your iTunes library.
You can find the full article here:
About Remote app for iPhone, iPad, and iPod touch
http://support.apple.com/kb/HT1947
If you are unable to connect to iTunes using the Remote app, I recommend following the steps in this article:
Remote app for iPhone, iPad, or iPod touch can't connect to iTunes or Apple TV
http://support.apple.com/kb/TS1741
Thank you for using Apple Support Communities.
Best,
Sheila M.