Can I transfer my sim card from my iPhone4 (no S) to an iPhone5S bought from Koodo? Also, I'm currently with Telus, where I bought the 4. I don't want to lose all the information currently on phone, like pictures and apps.
You can back that stuff up with iTunes. The 5s uses a nano Sim while the 4 a regular Sim so you'll either need to get it cut and gently see if it fit (Nanos are slightly thinner but in my experience the tolerances are forgiving) and if you're not comfortable with that you will need to get a new Sim card to activate on your account to switch to the 5s.