I am trying to give one of my users the ability to assign values in field dependencies. I believe that the permission they need to do this is "Customize Applications" however i can't seem to find this permission set within the "Systems Permissions" area which i believe is where it sits. Is anyone able to help with this ? (See screenshot below)
Salesforce Platform license does not allow that system permission. That's why you are not able to see that permission in the permission set. You'd need to either select Salesforce or leave the license type empty.
From the documentation:
These users are not entitled to some user permissions and standard apps, including standard tabs and objects such as forecasts, leads, campaigns, and opportunities. Users with this license can also use Connect Offline.