F-14 on the History Channel's "Modern Marvels"

A couple of night ago the History Channel aired a program about the
F-14. During the promo it was stated that the Tomcat is the world's
fastest fighter. I dunno, every aviation book in my house puts it
clearly behind the F-15 and the MiG 25.

Also, the program stated that the Shah of Iran ordered a fly-off
between the F-14 and the F-15 in order to decide which one he was
gonna buy. But when the narrator was talking about the Eagle, they
showed footage of what was clearly an F-5.

So, what's going on here? Am I wrong, is the Tomcat actually faster
than the Eagle. And what's up with the F-5 footage? Did the US offer
the Shah F-5s or F-15s? Did the documentary show the wrong footage,
or did the narrator misread the copy, or was he given the wrong copy?
When I get confusing information from a documentary it makes me doubt
the validity of the entire work.

Did anyone else see the program, or can anyone give me some clear and
unimpeachable facts?

Thanks in advance,
Brian J. McCann