Can I get an iPhone 5 without upgrade?

I've had the iPhone 4s for a while now. I had to use an upgrade about a year ago I think to get a new one because my first was broken. Just this last weekend, my 4s was stolen. Luckily I still had my mom's original 4 to hook up to my number.

Although I'm super grateful to have her phone, I'm incredibly into photography and it simply doesn't have enough space and isn't fast enough for what I want. I was hoping to get the 5c (much cheaper than the 5s), but I'm curious if it is even possible. If I can find a 5 to buy off of an individual person, could I do the same thing I did with the 4 and just hook it up to my number for free? Or since it's a newer version does it not work that way?

Hopefully one of you knows! And I hope I described it well enough.

No, your phone itself has an ESN number locked onto your sim card. This means even if you hadn't lost both your phone and sim card you couldn't hook the new phone up to your number anyway. This means without buying a new iPhone and line from your carrier you can't get an iPhone 5 that has cellular access.