Q: I have just bought an iphone 5 outright. For some reason without wi-fi turned on, I can't connect to the internet. Why is this?

Goto settings-->general-->cellular  and make sure 'cellular data' is turned on.  This will use your carrier's data plan when you have a cellular signal but no wifi.

EvoIX wrote:

Do I need a cellular account or something?

Well, as a matter of fact you do.

Can you make phone calls?  Yes, of course you need a cellular account. The data is part of a the plan offered by your wireless carrier.... it comes from the cell towers.

Well, if your phone is carrier locked, you contact the carrier the phone is locked to & establish service. They will then give you a sim card. If your phone is officially unlocked, you can use any carrier you like, but again, you need to contact them & get a sim card.

You need an activated sim from the carrier of your choice. If you want to use Optus, call them & establish service...pick a plan. Get an activated sim & you're off & running.