I can't download ios 6.1.3 to my iPhone 5

Details, please. How are you trying to update, and what happens when you try?

What happens when you try...?

If you are trying to use Over the Air and it is not working...

Connect to iTunes on the computer you usually Sync with and “ Check for Updates “...

If an Update Appears Install it... if not... you are up to date for your particular Device...

See the Using iTunes Section Here...

How to update your iPhone, iPad, or iPod touch

I can not update my ipad 2 (8.1) to ios 8.1.3. It just stuck when it was Extracting the sofware. I waited for 8hours but it still not loading.

Instead of bumping a two year old thread, you'll get more attention and faster responses if you start your own thread.

You also might want to post in the iPad forum.

Best of luck.