Q: iOS 9 just installed on iPhone 5. Can't get past "slide to upgrade" screen, tried hard reset, gets me back to same screen after entering passcode

See this:

If the Slide to Upgrade screen won't go away after you update to iOS 9 - Apple Support

This is BS apple!

This is a user-to-user forum, not Apple.

Its been backing up for 24 hours

If you're having trouble backing up (and this phone has never been jailbroken, see this:

iOS: Troubleshooting backup issues in iTunes

How am I supposed to do this if I cant get into my phone?

Restore using recovery mode as described here:

If you can't update or restore your iPhone, iPad, or iPod touch - Apple Support

im having the same problem with being stuck on the 'slide to update' screen, and i have looked up all the solutions for it, but they all involve connecting my phone to my itunes account (which my phone has been synced with my mac for a long time) but when i try to connect my phone, it says that i have to respond on my phone to allow connection. how am i suppose to do this if i cant get into my phone to do anything?

Use recovery mode:  with the phone connected to itunes, simultaneously press both the home and lock buttons until the Apple logo appears, then continue pressing the home button alone until iTunes detects the phone in recovery mode. You can then restore.