Of course you can.....
The docs do say that Magento doesn't support newer PHP...
The only issue you'll find that is easily solved happens with a change in the PHP interpreter dealing with Abstract class inheritance enforcement.
There are two files in the Zend library that generate PDFs & Images that need an extra function and parameter added and then its pretty shored up.
Just keep an eye on your logs, the files will jump out when you try to print a shipping label, or invoice.
I've had no problem running Magento on PHP 5.5 with this one consideration. 5.4 - 5.5 has minimal incompatibilities, none of which are found in Magento or associated libraries.
I have two Mage Builds running on my personal server on exactly 5.5 and 5.3.28, works great.
One is 22.214.171.124 and one is 1.8