Anyone could give me some tips how I upgrade Magento 1.5 to 1.9? I am new in Magento and I didn't see any upgrade option in my Magento backend.
Updating a Magento shop can be a complex task, especially if you have custom code and/or lots of extensions. Take a look at How do you give estimates for Magento upgrade? to get an idea.
Bottom line is, don't do it, if you are new to Magento development. Hire somebody with experience and don't be surprised if it gets expensive.
Exception: if your shop has no modifications and no custom theme (i.e. only 3rd party themes/extensions), you can download the latest version from http://magentocommerce.com/download, get the latest version for all your extensions, the latest version for your theme and hope for the best.
Important: Don't ever do this directly on a production server!