software Mac 0S X

Been trying for months to update my ituens software on my Mac 0S X 10.5.8

Keep getting this message below:

The iPhone” cannot be used because it requires iTunes version 11.1 or later. Go to www.itunes.com to download the latest version of iTunes.

I go to website, I download software but can not get the itunes install option to work?

Help please!! itunes is losing money by not helping me!!