Really simple question:
Can I use this cool Unity 5 splash screen:
instead of this boring Unity ~5.3 + splash screen:
with Unity free/personal edition? (Just because it looks cooler.)
You can only use whatever splashscreen unity provides you. You can change some color / timing settings with the new splash screen but you will not get the old one back.
The new one is much better once you add your own graphics to it, which you can with the Personal Edition.