To add a free license to your ESXi 5.5 installation, go to the VMware webpage and log in to your account. There you will find a „License & Download“ button, where you can register for a free license. You might also search for „Free products“ on the product webpage and click on „vSphere Hypervisor“ to get there.
The component is called „VMware vSphere Hypervisor 5 License“. Just enter your data and proceed and a license will be shown to your back on the web page.
After that, go to „Configuration“ > „Licensed Functions“ in your vSphere Client.
Open the options in the upper right corner.
When you save your key, your free ESXi 5.5 license will be enabled.