Amendment V specifies "no person", neither "no national", nor "no resident", nor "no citizen". Amendment XIV, extending this to limiting the individual states does restrict it to "citizens", but this is a case of the Federal government acting.
Also, the Privileges and Immunities clause has been interpreted as referencing citizens to define the class of rights being engaged by the amendment (those normally enjoyed by citizens), and not as a definition of the class of people to whom those rights are accorded.
Of course, Privileges and Immunities is also a weird zombie clause.
It doesn't mean "no person anywhere." The Constitution is a law. It implicitly limits itself to people under its jurisdiction. Historically, that has been defined territorially and in terms of nationality. You can even argue that US citizens have no Constitutional rights off US soil though it was decided otherwise by the Supreme Court.
You've refuted yourself; tens of millions of non citizens are subject to its jurisdiction. Clearly it's not limited to citizens, nor does it say it is. People subject to its jurisdiction seems the more apt interpretation.
That's why I said Americans instead of citizens. In the extraterritorial context, citizens are the interesting category. Citizenship follows you around when you're in Yemen for decades. US residency doesn't.
