Should I get a case for my iPhone 5?

Because it needs protection; I dropped my previous iphone and the screen cracked.
However I feel that it looks more beautiful without a case.

Yes you should. I recommend the otter box. Wonderful cases! Here is the website: http://www.otterbox.com/

I think you should get a case for it. I prefer it without a case as well but it's better that it's protected. There are many awesome cases out there so your iPhone will still look cool with a case!

Put it this way, do you want it to just look good or do you want it to work properly. As you said you already broke your last one so you most likely will this one too if its not protected.

No take a chance without the case. Anyways it did not cost a lot

If I were you, I'll buy it and I'd go for Barely There from Case-Mate.

I bought this because I wanted the most unobtrusive case I could get. I didn't want to add any bulk to my iPhone, so the phone looks awesome. The case is very slim and light and does a nice job of protecting the phone as well as the buttons and the back. It's very unobtrusive and wraps around the phone very tightly, like it's part of the phone. Other cases can give a bit when you squeeze or don't quite grip right, but this one is perfect.