I agree with Jennifer - relying only on numbers will cause confusion. Be prepared to ask for clarification.
If you have other dates from the same writer, you may get a clue as to which system they use: 06/05/2010 =??, but 06/19/2010 from the same person tells you the month comes first.
The difference is if you say the "6th of May" (=06/05/...), or "May 6th" (=05/06/...) in speech. Going by "American style" or "British style" gives you a good indication as this is how date-order is taught in each school system.