When it comes to official profiles for Shadow, you're going run into this a lot. It's common for them to either completely avoid listing an age or list it as something to the effect of "unknown."
I don't think Shadow has ever had his age officially listed as "50+" or "Immortal," although his immortality and backstory will obviously be mentioned on certain more fleshed out profiles. The "ageless" descriptor you see thrown around technically has some official use, but the main source for this, and what Sonic Wiki Zone cites, is a character guide published by Scholastic of all things.
Here are some links to English sites that appear to have been archived with little to no hitches: [X] [X] [X]