I need to know the top 5 internatinal airlines that bring passengers
to and from the U.S. Also, what were the 2004 enplanement (# of
passengers) brought to and from the U.S. on these airlines?

Lynnh --

At one time the Research and Special Programs Administration in the
U.S. Department of Transportation published a report called "U.S.
International Air Travel Statistics."  While it didn't list individual
carriers, it did show U.S. and international flag carriers and
arrivals at each airport from each country.
(If you were familiar with carriers that served each airport you could
deduce volume by carrier.)

Since sometime in the mid-1990s that survey has been taken over by the
Travel Industry Association of America (TIA), which sells it for $500
per copy.  They have a number of research products, but I think that
their most-recent data on international arrivals is for 2003.  Here's
a link to their research publications page:
TIA
"Research"
 http://www.tia.org/Travel/travelforecast.asp

You may wish to check the Bureau of Transportation Statistics at the
DOT but in my research to attempt to answer this question I found
nothing relevant to your question.

Best regards,

Omnivorous-GA