Is there a limit to how many iOS devices I can synch with iTunes?
There is no limit to how many iOS devices you can sync with iTunes.
The 5 computer limit is how many computers you can have authorized simultaneously with iTunes.
I'm pretty sure this has changed now. Apple updated their policy in August '11.
http://applenapps.com/apple_news/apple-quietly-updates-itunes-policy-to-reduce-the-number-of-authorized-devices-per-account.html
I've had no issues syncing 300 devices with one library.
Other than disk space to track the backups of each device, your time and money, I don't think there is any pre-defined limit.