IPhone 5 Turns Off With 20 - 40% Battery Left

I've had my iPhone 5 since April 2013. From the start I knew I'd have to accept that the battery was going to drain quicker than I was used to, but I was prepared to accept it due to knowing that I was getting a high quality phone.Â

Things were as expected until 3 or 4 months ago. Since then, if my phone doesn't get used for 3-4 hours it can go down 5-6% (as I would accept), however, when I am using it, it shoots down. I can go to work at 9, finish at 5 and have 80 odd percent left. By 6, once I've had some basic usage, it can be down to 50%. This is far quicker loss than I've experienced in the past. This has included dropping by 10-15% in one instant as has happened on numerous occasions.Â

A further issue is that my phone can be displaying up to 45% battery (the highest it's happened) and turn off when I'm using it. If I try to turn it on it says that I need to plug it into a power source. If I leave it 20-30 minutes then it will turn back on and say that I've got the amount of battery that I was supposed to have when I turned it off. If I use it to do nothing but check the time it stays this way, if I try to use any other function then it turns off after 30 seconds or so. Once I get it plugged in (from being 'dead') it will start charging from 20/30/40% (wherever it went off at).Â

Particularly if I know I'm going to be out for a while and won't have access to a charger. I can't base what battery the phone's telling me I have on what I actually have to use. I always close apps after I've used them, background app refresh is off, I only have wi-fi running regularly (no bluetooth, mobile data, 3g etc.)Â

Info:
iPhone 5, iOS 7.1.2