Q: NEW iPhone 5S and now iTunes WON'T sync

Reboot both the computer and the phone.

I'm having the same issue.  After updating to iOs 8 and then updating my iTunes, my iPhone (5) would no longer connect to iTunes.  The computer recognized it but not iTunes.  I had to update the drivers in device management to get my phone to finally appear again in iTunes.  Now, I can't sync my phone because I keep getting this computer not authorized message.  I've de-authorized and re-authorized my computer a bunch of times and still my phone will not sync. 

The best part is all of my purchased songs still work but yet say I have to re-authorize the computer?  Anyone else find a fix yet?

I am struggling with the same issue. Tried everything but it doesn't seem to work.

I'm not sure exactly which issue you are having problems with.  If it is that iTunes does not recognize your iPhone, try this link:

<<If iTunes doesn't recognize your iPhone, iPad, or iPod - Apple Support>>

If it is that iTunes does not sync with your iPhone, then this might be helpful:

If you are getting the repeated prompts of asking to authorize your Apple ID, then check out the article below to resolve the issue. Make sure that you go through and remove the SC Info folder and try to authorizer again as that resolved it for me when I had that issue.  

iTunes repeatedly prompts to authorize computer to play iTunes Store purchases

http://support.apple.com/kb/TS1389

I checked Itunes is up to date and it does recognize my phone when i connect using the USB cable. My problem is over wifi. I cannot sync over wifi.

Try this first: Go to Control Panel > Programs and Features > find the apple mobility device support > right click and hit repair.  Then see if WIFI syncing works.

If you still have issues:

Sync your iPhone, iPad, or iPod touch with iTunes using Wi-Fi - Apple Support