What OS are you running? Since you mentioned PHP 5.5.9, it sounds like you might be running Ubuntu 14.04 (Trusty), which is a LTS release.
Unless you're using a 3rd party package (like a Ubuntu PPA) or compiled PHP yourself, 5.5 isn't suddenly going to stop being supported.
CentOS/RHEL or a Ubuntu LTS release all have long term support that backport any security fixes if necessary to the older distros. (What's confusing is you might be getting security fixes from, say 5.5.34, but the package maintainers don't bump the version because you're not actually running it. This is a common false positive in PCI compliance scans, for example.)
In these kinds of things, I would spin up a VPS or fire up MAMP and test the install yourself. While Craft itself runs fine in my experience, you could run into trouble with plugins.
That said, I'll echo Lindsey's answer and agree that PHP 7 screams. Skip the 5.x branch if you're not running any other software and jump on 7 if you plan to upgrade because you'll be upgrading to it at some point anyway.