Do I need a new iPhone 5 battery?

How do I know if the jailbreak is messing up my battery or if I need a replaced battery? I can go to bed with my phone in the 90% wake up and it will be on 1% sometimes! Then when it's on 80% or in the 70% range it will go off and say its dead but once I plug it back up, it comes back on to 70% range or the 80% range. I'm seriously about to break my phone! It's a iPhone 5 also if that helps!

Updated: Today it went of on 93% and said it was dead. I plugged it up and it came back on and said it was 88%.

I guess so.