THisis not recommanded to COPY the config from 4400WLC and upload to new WLC 5508.
Do not download a configuration file to your controller that was uploaded from a different controller platform. For example, a Cisco 5500 Series Controller does not support the configuration file from a Cisco 4400 Series or 2100 Series Controller.
But but..... I think Cisco doesn't support it, but it does work. To easiest way to get one config to the other is to take the config from the existing and putting it on the new wlc. Now the new one will be offline, so when you do this, you can always verify that the configuration is identical. Of course the part of the configuration that you will have to change is the hostname, mobility information, maybe ip address.then you can change from GUI .....It will work
If you copied from 1wlc to another then you have to lokk for may thing taht what is right or wrong.
BUt If you beleive me then do the config from scratch for 5508 WLC.
The only real way you can take a config from a 4400 and upload it to a 5500 is to make sure that both are on the same code version. So put both on v22.214.171.124 and export the backup from the 4400, now you need to edit the file by opening it up in a text editor. The username and password you should remove and manually enter those in plain text. Remove other lines if needed. Make sure there is a trailing space at the end of each command also or else it will not be used. You can then restore this to the 5508 assuming you already went through the startup wizard and you have access to this WLC through the network or service port. This will get most of what you need, but you need to review it after you upload it to the 5508. Go through the GUI and verify that things have moved properly. After you verify this, then you can upgrade the code to what you want and also make sure you have the latest FUS image installed or else install that too.
This isn't a process for those you doesn't understand the CLI commands and know what you should remove because of the difference in the platforms. If you have the WLC in a lab, then why not practice if you have time and see if it works for you or not.
Like Sandeep mentioned, it might be better for you in the end to build it from scratch.