Is it okay to start charging my iPhone 5 when it's at about half battery?

I used to have an iPod, and the battery got kind of messed up, it drained really slowly and charged really fast. But I just got an iPhone 5 and I don't want that to happen again, so I usually try and drain the battery until it shuts off. But sometimes I stay up really late trying to drain the battery so that I can charge it fully for the next day. But is it okay to start charging it at about half battery?

Try to charge any phone battery when battery level it falls below 15%
it increases battery efficiency and increases battery life

Draining the battery before charging does NOT affect the battery life of the phone. You can charge the phone whether it's at 5% 50% or 85% and it won't make a difference. I've used an iPhone for over a year and charge it every night regardless if I use it much during the day or not. Some nights it's at 20% and others it's at 75%. The battery has remained the same. The only thing that would affect the battery life is exposure to extreme temperatures or moisture.

Don't worry about charging your iPhone 5, just charge it whenever you feel like it! A good option is to charge your phone every night so it will never die during the day.

Yes sounds quite reasonable to me

Yes, thats fine.

Thts normal