My iPhone 4 would usually make it through an entire work day with a bit to spare. Today I have 2 hours left until my work day is over and my iPhone 5 is at 14% as I write this post. Being that my iPhone 4 is old as hell, I figured I would at least be getting battery life on par with the 4 on my 5.
1. Was this expectation wrong?
2. How can I tell if I maybe have a bad battery?
first of all, you're being very vague. We don't know what you're doing with your iPhone.
With an LTE phone, you're going to use more data, because it's quicker, and therefore you'll do more with it. Streaming audio? Well, it'll be streaming audio at a higher quality. Streaming video? same thing.
Also, there are a ton of things you can do with your iPhone 5 to improve battery life. Go into location services and turn off the apps that don't need it (you should only really need it on maps and weather) and turn off push notifications for apps that you don't want to be notified about (most games will ask if they can send you notifications, which are always ads)
Go into privacy > location services and scroll down to system services. You don't need location services for most of those, except cell network search.
I turned off a lot of these, calibrated my battery, and my battery life was much improved.